Welcome to the forum.
You are right in the post-op swelling phase. After the surgery you feel better for a few days and then the swelling starts up. It goes away gradually, so don't panic! Above all don't let them stretch your wrap! This will pass,although it can take days to weeks, and even a couple of months won't be fun.
The only time to worry is if you can't get any liquid down at all, zero, none.
You had a bunch of stuff shoved down your throat, so it hurts while it heals. Besides the breathing tube, there was a bougie that was used to keep the wrap from being wrapped too tight. There were probably also other tools.
I had trouble with plain water, but slippery soup with no chunks at all went down. Same for drinks. Orange juice burned for a while. Milk was great, also provided lots of protein.
I didn't tolerate anything solid for a month or more. Baby food - very smooth pureed food, thinned went down. Even adult apple sauce was too rough for a while.
You could look at this diet that is often recommended:
www.upmc.com/patients-visitors/education/nutrition/pages/diet-after-nissen-fundoplication-surgery.aspxIt gets better!