Thanks for the replies. Nope, I won't be doing that again. I'll just gag and retch and puke for days until it comes out on its own, because apparently that's the only other option.
I tried the qtip and soft toothbrush because those are actually things that doctors have recommended for very stubborn stones. There's a certain way you can use them to "gently" scrape out the stones, which is what I tried to do. I've never had to try it in 20 years because I've always been able to just wait them out, and plus I really hate to gag. But this one was already making me gag frequently and throw up (once), so I felt I had to try it.
The stone did come out after I gargled with salt water all night. Immediately after it came out I stopped gagging and the swelling went away. So I didn't rip up my throat, it seems the pain/swelling was caused by all the gagging. It makes sense now that I think about it. The qtip never touched my uvula.
I've heard of people using toothpicks, or even paperclips to loosen stubborn stones, but those aren't doctor recommended and I wouldn't trust myself using them. Waterpiks are also recommended, but they're kind of expensive. Still might be worth buying though.
I just hope I never get it this bad again. That was AWFUL.
I mean sorry for posting here freaking out over something that must sound so insignificant, but I've had cancer scares that were less traumatizing to me than this. It was really, really, really bad.