This doesn't really sound like you're choking as much as you're potentially forcing too much fluid into your stomach causing regurgitation. It sounds like you really chug a lot of water to take those pills.
I usually take my 4-5 morning vitamins with about 4-8 oz of OJ and I will sometimes span the pill taking over a few minutes (I am pregnant and the gag reflex is awful right now).
I think true choking is when food gets lodged in your windpipe preventing inhalation or exhalation. I've done this twice in my life and it was absolutely terrifying. I noticed that both times it happened, I was talking and socializing while eating rather than focusing on bite proportions and chewing. I'm much more careful now.
My recommendation would be to drink the water slowly over an extended period of time so your stomach has time to push the liquid through to your intestines before putting more water in.
Good luck!