Impatient is putting it mildly! You just had the surgery! If you had irritation, that irritation will take some time to subside.
Your wrap is swollen, and it's very likely that your esophagus contains retained liquid after you eat/drink. Therefore, if you burp, it pops that liquid up into your mouth. That happened to me all the time after I had the surgery. I worried, but when it wasn't acidic, I relaxed about it. It's just whatever is in your esophagus getting blown back up into your mouth by gas releasing. People who can't burp don't have that experience.
Relax and let your recovery lead you. Don't stress and try to put your recovery on a time line. As Joy said, you'll look back on this anxiety, and wish you hadn't made yourself crazy with worry and anxiety. It's not worth it. You can't rush the process, Joe. It will happen when it happens. Stop stressing!
As far as the PPI's...I stayed on them during recovery. Some people don't. It won't hurt you to use something. As I said in an earlier post, during the early stages of healing it's possible that you could get a little reflux. Many do.
Stop worrying and relax!