Bla.... You know I had a similar problem with my first...Matilda. My brother teased her & she hasn't been right since. She actually has a fear of strangers touching her & will bite if picked up. Fear aggression basically. She's gotten more comfortable with age & loves when my girls have friends over. She'll even sit in their lap and let them pat her--but I'm always sure to tell them to not try to pick her up. If they pat her...and she doesn't fully trust them yet, she'll just run away not bite or anything like that. She just bites when she feels "trapped".
I've had more issues just like that with my pets from the same breeder honestly. I seriously think it has a lot to do with their first 8 weeks & the interaction they get. That besides the point.... Evie went through a weird stage between 5-10mo. She is from an entirely different breeder btw. Since she's had her first heat she's completely mellowed. I even took her to my work (Alzheimers unit) this past weekend where she stood willingly while people patted her & some of the residents even held her w/o issue.
Since I want to show her...and she really NEEDS to be ok w/handling I've been working quite hard since she entered this weird phase to get her out of it. Things I have done to help is going & sitting in the middle of our town during 5pm traffic. Just sat there...for an hour at a time. Just ignored her while she was on her leash (usually hiding under the bench I was sitting on) & let her work her issues out herself while the noisey traffic/people passed her by...sometimes stopping & looking/talking to her. I never let anyone pat her in that situation because she was obviously shaken up & I didn't want to put her over the edge completely. I wanted her to know it was OK to be overloaded with all senses and still be SAFE. I've taken her to stores & just walked around. Had people give her treats. I took her to shows & handling classes where she was forced to be handled a bit by others. Of course I had to have tight grip on her stacking her as she wasn't thrilled with it. There was one person that went over her at class once where she freaked out & tried to bite. Just that one certain person. I held her & the person continued until Evie at least tolerated it. So she knew that biting wasn't going to get her what she wanted. I also sent her to our breeder friends house for a couple weeks. She has company ALL THE TIME. So she worked with Evie there, she & her neighbor took her out & about, etc. Basically...she had to learn how to trust strangers while there. All this sounds kind of mean/out there but in the long run...it will make her a happier, more well adjusted adult Chi. And she's already proven to be more comfortable in different situations. I am sure having a heat helped her mellow a bit but I still feel all we've done to work w/her in the process has made her come so far in such a short time. She is 11mo today btw.
I don't know if any of this helps. Having a couple Chis with people issues I know how stressful it can be. Basically you have to expose them SAFELY to people/contact. Safely to them..and safely to others. Its funny but when I bring Evie into a store & say kids want to come see her...I stack her on the floor so I have a hold of her front/head & rear...and just ask them to pat her back. If she even thought about biting (which she never has-except that one time at class) she wouldn't be able to move enough to.
You say you have Tiki in a bag...I having her walk on a leash will be helpful when you go out/about. At least in stores that allow it. And definitely always outside/on the sidewalk of town, etc. Also, if she's ever "protecting" you when you're approached...put her down! Chis very easily get possessive over their humans if not given strict boundaries. Good luck...I hope you are able to work with her a bit & get her out of her little funk.