It is a weird disease, and burping sucks. What's even worse is when you CANNOT burp. Now that's bad. That's why I mentioned the simethicone. It should help you have "productive" burps to get rid of the gas, in theory.
I've read a lot about swallowing air in the past. Some people do it when they eat too quickly, and for some reason drinking with straws supposedly makes it worse. I have no idea why that would be.
My GERD has lessened in severity recently but I still go through times where I burp a lot or can't burp and need to. Never really found an answer for it. I do know it's worse when I eat quickly, so eating slowly and trying some simethicone is the only advice I can give you, unfortunately.