Katy...

I wouldn't go so far as to say that wheat and other grains cause stomach ulcers, but a lot of people who have had chronic reflux and indigestion along with other intestinal problems such as irritible bowel syndrome (IBS), diverticulitis, crohns disease and such have reported a great increase in relief when they cut grains out of their diets.
Low carbing is also no guarantee that you won't develop stomach problems as there are other factors that can be at work here as well such as stress and sometimes just a genetic predisposition to it. I'm not sure how often you need to eat broccoli for it to be effective against h. pylori, but I'll do some checking on it.
Whenever I've had problems with my stomach, the first advice I was given is to avoid spices, caffeine and carbonated drinks. It might help if you cut out the tea and coffee for a while or substituted an herbal tea instead. Chamomile and mint are both very soothing to an upset stomach.