Sorry to hear that. Were you recently diagnosed, or have you been taking antibiotics for a year and a half? If the latter is the case it is an unfortunate problem. Hopefully you don't have a particularly resistant strain of bacteria. An unfortunate side effect of blanket prescriptions of antibiotics is that bacteria have a tendency to mutate into forms that are resistant to the drugs.
I'm not trying to make you feel worse, just throwing out an idea. I'm not a medical professional.
What do you want to know? You seem to have a solid grasp of the basic idea. H. pylori weakens the stomach lining allowing the roiling pit of acid inside your stomach to attack the outer part, which the lining protects. Gastric acid (stomach acid) is very, very acidic. Essentially, you are digesting your stomach. Not a good thing. That damage will allow other opportunistic disorders to occur.
That's the basic idea outlined in
this wikipedia article. The mumbo-jumbo basically outlines the actual mechanism the bacteria uses to replicate and attack the stomach lining, most of which you don't need to know.
I sincerely hope your doctors find a method of treatment that works for you. H. pylori can be wiped out, it just may take more work than usual in your case.
One small thing you can try. The article suggests that broccoli sprouts and green tea may help to inhibit the bacteria. I usually find these claims fairly dubious, but it can't hurt to try, especially considering both foods are good for you anyway and are quite tasty. (At least I think so.) Those two alone won't kill the bacteria, but it may help you feel better.