Hi Alynn, I try to just say "I don't drink" but when people won't accept that, I've given the following explanations. They are all true for me, but you are welcome to them if you think they would work. I know it is a royal pain in the ass when people won't accept a simple "I don't drink."
"I can't drink with the blood pressure medications / heart medications / allergy medications I'm on." (If it's a group that has any kind of sense of humor, I have found that humor can be really effective to defuse and deflect… sometimes I'll add a joke at the end and then shift the conversation. Something like, "unless you want to scrape me off the floor.").
When people push for an explanation I've also told them I can't drink because of stomach problems. That's also true for me.
With either explanation, if they insist that you really CAN drink, you can tell them you'll puke. On them. That's usually a conversation ender.
I've also gotten people to stop pressuring me to drink by saying something like "I don't drink. I know you guys will understand that and I really appreciate your understanding." You can lay it on with varying degrees of thickness along those lines. Some people have no shame, but with others I've gotten this to work.
If you really wanted to shut people up you could probably tell them you don't drink for religious/spiritual reasons, which if you're in AA, I guess you might consider to be true.
Good luck!