I've done countless blood test and H. Pylori test 2 times, everything seems to be fine. I'm sure yours came out OK too. But he's treating you by the symptoms rather than the actual test results, correct?
My symptoms are almost identical to yours minus the gas from the mouth thing.
My visits to doctors usually ends up with more frustration. I actually went to a naturopath a couple of months back, which consists of 2 sessions totalling 3 hours. In both sessions, I find myself trying to convince him that I have this issue and he's saying that he doesn't smell me at all.
The 2 days that I had the session with him, I went to the mall immediately afterward and try to interact with some of the clerks who work there to see if I'm indeed smell-free. But sure enough, I get the usually coughing and nose-rubbing gestures. And as expected, the next day at work, I got the usual violent coughing, nose-blowing and comments like 'someone farted'.