I'm having pretty bad morning sickness and I also have the burping problem, but weirdly enough it actually seems to settle my stomach when I'm feeling really sick!! One morning when I was feeling absolutely gross, I forced myself to drink a glass of soda water (which wasn't easy at the time!) then a couple of minutes later, I let out one huge burp and I didn't feel quite so nauseated after that!! With my previous 2 pregnancies, I found that the burping phase was worse in the last couple of weeks after every time I ate anything!! Good luck.
Belinda.