I have hiatus hernia and Lansoprazole works great for me. Omeprazole/ Losec is the same kind of drug and should work. There are varying doses to try. Have you had an endoscopy - (camera down throat) This was what diagnosed my hernia
The H Pylori is a bacteria which will cause ulcers which can also give you the heart burn side effects you are describing. It can be detected in a blood test. If it is positive you can be treated with High dose antibiotics and H 2 Antagonists/Proton pump inhibitors for about 10 days I think. It can be a bit unpleasent- nasty taste in mouth I think. But will work
But if it where me, I would ask for an endoscopy. Again not pleasent, but I had no sedation silly me was frightend of the needle
DS had really bad reflux as a baby, couldn't lie down, had to sleep sitting up, was on multiple medications, etc. In desperation we brought him to a Cranial Osteopath, and she cured the reflux, it was amazing. We were bringing him regularly for treatment, twice a week in the beginning, over a period of months, but the improvement was obvious after the first treatment.
If you have been suffering for this long it might be worth a try.