There's no reason you can't show your pup. It's fun, but can get expensive over time. I'd say, go to some handling classes if they are available in your area and enter a show or two. While at the shows talk with the chihuahua people....maybe someone could take a look at your pup and evaluate him.
I showed my maltese even though she was too small to have pups (the breeder knew me and let me show her just for fun). Some people told me I was ripped off by the breeder (lol)
....but she took "Best of Breed" in one show...so you never know.
Now I'm showing Mona Lisa and her breeder sold her because she was too small also....so here we go again....she's letting me show her. I'm not into it to take the show world by storm, and some owner/handlers need me so they can get a point.
....who knows, maybe we'll get a point one day.... Mona Lisa also had an arched back and walked like a weasel, I started feeding her Dr. Harvey's morning and evening and she put on some weight, now she's walking beautifully!! Yeay!!!!