I also burp alot!!!!! and deep, loud!!!! I have had enthroscopic proc., colonoscopy--I have gastritis. I am waiting on the biopsy of the stomach to why I have gastritis and I have level B GERD. Next week I am going in of a HIDA scan for my gall bladder-my Doctor feels it is not working and bile is backing up in my body. Ask your doctor to check for these things.
I didn't see you mention them checking on your gallbladder. Burping at times can be related to a problem with that, I've read. Did the doctor ever suggest IBS regarding the flatulence? Did they put you on medicine for the acid reflux? Did they test your TSH? Did they make sure there was no problem with your heart/circulatory system regarding your fatigue and severe headaches? Did they check you for parasites?