Hello~I have had that shortness of breath and the feelings you have with it as well. It is usually when I am stressed or anxious and the more I worry about the worse it gets.
If this continues, I would see your GP, he/she will be able to run any tests that are needed and will be able to rule out anything that might be serious.
Also, and I know this will sound crazy, but a chiropractor might be able to help. You may have some pinched vertebrae in your upper back causing the shortness of breath and even the continuous burping, it sure wouldn't hurt to see one if you are able to.