Where did you hear that listerine and or hydrogen peroxide will increase your chances for oral cancer?
I too have a small bump behind my lower teeth, I've had it for about a year now, seems to be getting slighly bigger each month.
In addition, I also use hydrogen peroxide daily, listerine at times. My dentist told me hydrogen peroxide is fine to use daily, actually good for your oral health, as long as you use half peroxide and half water.
The hard bumps sounds like Tori if the dentist told you that its nothing to worry about. Tori just means you have extra bone growth, which wont hurt you, and many people have this. The only time it ever affects you is if it interferes with function. If it goes so far to interfere with function then you would just have it surgically removed.
Also, be careful of using hydrogen peroxide for daily use because there is a lot of controversy on long term affects on your oral tissue and enamel. I have only heard it recommended to use when there is an actual infection present like periodontitis. Do some research on it and make your own decision.