How are you drinking? Normal-size drinks? Or teeny sips? Smaller sips can help.
I'd also suggest trying different temperatures. Hot, cold, room temperature. Some people have better luck with warm water (or broth or tea) sitting in their stomach.
Sparklekitty / Julie / Nerdy Little Secret (#42)
Roller derby - cycling - triathlon
VSG 2013, RNY conversion 2019 due to GERD. Trendweight here!
I haven't been able to figure out what to do physically to control how much air I swallow. But I have found that if I pay attention when I'm drinking, I take in less air. Conversely, if I drink absent-mindedly while doing something else, I take in more air. Perhaps that will help you.
But I don't think you need to worry about it at this early stage, unless it's causing you pain. Right now all sorts of weird things are likely to happen while you're healing from surgery. The problem may disappear entirely in a week or two. I know I suggested that swallowed air might be the cause of your problem, but it may simply be excess acid produced by your stomach.