I don't know if it'll help, but right out of surgery I found my "sips" were a bit too big. I definitely felt like I was sipping, but then I'd get the air bubble feeling like I have to burp, and trying to force myself to burp would make some liquid come up too, so I'd have to swallow again, then burp, and repeat several times in order to get the air out. I think maybe since I use to gulp water prior to surgery, my sense of a sip versus a normal drink was off, and I was drinking more normally rather than sipping.
I eventually did what @Creekimp13 suggested and repurposed our shot glasses into water cups, set myself a timer and made sure I was drinking an ounce over 15 minutes rather than drinking 1-2 ounces in a few minutes and then nothing for the remaining time.
Sitting up when sipping helped a bunch as well. I noticed when I tried to sip while in bed at night, it was much much more common to get the bubble feeling. It did get easier as I got further out, and I can take bigger sips at 3 weeks out then I could at 1. Still sometimes do one too big and get the bubble, but far less common now.