I remember reading that H. Pylori can be transmitted by kissing. If it can also be transmitted by sharing drinking glasses, food, etc, then I can see someone could say it was "hereditary". When my kids were little, they were always taking bites of my food and vice-versa.
Many people get rebound heartburn after stopping acid reducers. It can last for a while. When I stopped taking Nexium, I had terrible heartburn for about 2 weeks. It was much worse than before I started treatment. After a few weeks, I went back to normal. I had to stop the Nexium because I wasn't digesting my food while taking it. It increased my reflux, but it was undigested food coming back into my throat (and mouth, yuck!).
I found digestive enzymes and probiotics, plus dietary changes to be very helpful with the bloating, burping, and pressure. I'm still working on it but it is better.