In puppies there are two fear imprint periods; during the 8 to 11 week age range and again during the 6 to 14 month age range. If anything traumatic happens to the puppy and the fear is not resolved before leaving the imprint stage, the fear will be more profound and long-lasting than if it had not occurred or had been resolved.
Developmental Stages
It sounds to me like your puppy has a sensitive personality type and may have been pushed too far too fast during socialization and so she's learning to avoid people/places/things that she perceives as scary.
To start, she needs to learn to be more independent. When you are walking around the house, don't allow her to be your shadow 24/7. If you walk from your bedroom to the kitchen to get something to eat and she usually follows you, close your bedroom door to keep her in the bedroom until you return. If you do it enough she will learn that you'll only be gone for a few seconds and so she has nothing to fear. You not being next to her every second of every day won't be as scary for her if she's used to doing it every day. But you have to do it every day for her to get anything beneficial from it! (This is usually harder for the owner than the dog, I've noticed.)
This goes hand-in-hand.. but.. as long as it's not dangerous for her to be on the ground, and if you think that she will make progress in overcoming her fear (slowly approaching people, getting more bold, etc.) then make sure she's on the ground and NOT in your arms. Holding her will reinforce her fear.
Set her up for success, though. Keep her out of situations that she can't handle (ex. too many people or dogs in the room) and limit her to situations where she can make progress slowly (ex. one new dog or one new person). If she's shutting down then she's not only failing to make progress, she's actually creating negative memories from that experience. Remove her from the situation immediately if that happens and then redirect her focus to something positive. If the situation could put her in harm's way or if you think that she's so overwhelmed that she's in no place to make progress at that point then your best bet is to 1) leave, or 2) keep her safely in your arms (assuming you can't leave). For example, there may only be one new dog present for her to meet, but if it's an aggressive or really excitable dog, then having her meet them could significantly set back her progress. In that situation it's better to just avoid the dog entirely if you can.
Start obedience training using positive reinforcement. Look up clicker training or get an APDT certified trainer to help you. I usually tell people to stay away from Petco/Petsmart training classes because I feel they're a waste of money for what you get. You could learn to do all of what they do just by following your own research online. There are YouTube videos that help with some behavior problems (KikoPup is a good channel) and they give good instructions.
Get her out on a daily walk for at least 15 minutes each day. Expose her to the outside world but not necessarily to crowds of dogs or people. Try to take her to a new place or in a new direction each time, or in new situations (ex. rain/sunny, nighttime/daytime, nature trails/sidewalks, etc.). Just getting out of her "safety zone" and seeing something new every day will help her to become excited about the outside world. Allow her to explore things while on leash and if it's safe let her take the lead on occasion. It will show her that the world is a fun place to be, not a scary place.
I think you need to lower your expectations for this pup. That doesn't mean stop introducing her to dogs, but it may mean that puppy school is the wrong environment for her. She could maybe start with one or two calm puppies to play with. If there are any in your class you can ask the owners if they'd like to get together for a smaller play session sometime during the week. She might just be overwhelmed by all of the commotion of the other puppies playing.
But like I said above.. I would concentrate largely on building up her confidence and making her more independent. When she is cowering under your legs, get up and move away, ignoring her. Don't give her eye contact, don't reassure her with your voice, don't pet her. It may seem cruel, but the more you coddle her the more you're telling her, "That thing IS really scary! I'm so sorry that you're scared! You're right to be scared of that thing!"
PS: Did you get her from a breeder? Unfortunately low distress-tolerance is a common problem in puppies that come from breeders because the environment is often very safe and structured, with no stressful obstacles to the puppy. A great breeder will not only provide all the requirements to raising a physically healthy puppy (food, water, veterinary care, shelter, etc.) but they also handle their pups every day to make them emotionally healthy as well. There's a routine they can follow where they hold a pup in different positions to cause a low amount of distress, and by doing it every day the puppy learns to self-soothe and better handle a stressful environment when they're older. It's called the "Bio-Sensor" or "Super Dog Stimulation" program and it was developed by the United States Military for canine units.
Bio-Sensor-Super-Dog-Program
Developmental Stages
It sounds to me like your puppy has a sensitive personality type and may have been pushed too far too fast during socialization and so she's learning to avoid people/places/things that she perceives as scary.
To start, she needs to learn to be more independent. When you are walking around the house, don't allow her to be your shadow 24/7. If you walk from your bedroom to the kitchen to get something to eat and she usually follows you, close your bedroom door to keep her in the bedroom until you return. If you do it enough she will learn that you'll only be gone for a few seconds and so she has nothing to fear. You not being next to her every second of every day won't be as scary for her if she's used to doing it every day. But you have to do it every day for her to get anything beneficial from it! (This is usually harder for the owner than the dog, I've noticed.)
This goes hand-in-hand.. but.. as long as it's not dangerous for her to be on the ground, and if you think that she will make progress in overcoming her fear (slowly approaching people, getting more bold, etc.) then make sure she's on the ground and NOT in your arms. Holding her will reinforce her fear.
Set her up for success, though. Keep her out of situations that she can't handle (ex. too many people or dogs in the room) and limit her to situations where she can make progress slowly (ex. one new dog or one new person). If she's shutting down then she's not only failing to make progress, she's actually creating negative memories from that experience. Remove her from the situation immediately if that happens and then redirect her focus to something positive. If the situation could put her in harm's way or if you think that she's so overwhelmed that she's in no place to make progress at that point then your best bet is to 1) leave, or 2) keep her safely in your arms (assuming you can't leave). For example, there may only be one new dog present for her to meet, but if it's an aggressive or really excitable dog, then having her meet them could significantly set back her progress. In that situation it's better to just avoid the dog entirely if you can.
Start obedience training using positive reinforcement. Look up clicker training or get an APDT certified trainer to help you. I usually tell people to stay away from Petco/Petsmart training classes because I feel they're a waste of money for what you get. You could learn to do all of what they do just by following your own research online. There are YouTube videos that help with some behavior problems (KikoPup is a good channel) and they give good instructions.
Get her out on a daily walk for at least 15 minutes each day. Expose her to the outside world but not necessarily to crowds of dogs or people. Try to take her to a new place or in a new direction each time, or in new situations (ex. rain/sunny, nighttime/daytime, nature trails/sidewalks, etc.). Just getting out of her "safety zone" and seeing something new every day will help her to become excited about the outside world. Allow her to explore things while on leash and if it's safe let her take the lead on occasion. It will show her that the world is a fun place to be, not a scary place.
I think you need to lower your expectations for this pup. That doesn't mean stop introducing her to dogs, but it may mean that puppy school is the wrong environment for her. She could maybe start with one or two calm puppies to play with. If there are any in your class you can ask the owners if they'd like to get together for a smaller play session sometime during the week. She might just be overwhelmed by all of the commotion of the other puppies playing.
But like I said above.. I would concentrate largely on building up her confidence and making her more independent. When she is cowering under your legs, get up and move away, ignoring her. Don't give her eye contact, don't reassure her with your voice, don't pet her. It may seem cruel, but the more you coddle her the more you're telling her, "That thing IS really scary! I'm so sorry that you're scared! You're right to be scared of that thing!"
PS: Did you get her from a breeder? Unfortunately low distress-tolerance is a common problem in puppies that come from breeders because the environment is often very safe and structured, with no stressful obstacles to the puppy. A great breeder will not only provide all the requirements to raising a physically healthy puppy (food, water, veterinary care, shelter, etc.) but they also handle their pups every day to make them emotionally healthy as well. There's a routine they can follow where they hold a pup in different positions to cause a low amount of distress, and by doing it every day the puppy learns to self-soothe and better handle a stressful environment when they're older. It's called the "Bio-Sensor" or "Super Dog Stimulation" program and it was developed by the United States Military for canine units.
Bio-Sensor-Super-Dog-Program