I think my gums are infected, so i floss and rinse with peroxide and it stings and my gums and inside my jaw turns white and swells up.

Get checked: hydrogen peroxide needs to be diluted at least 50% if it is going to be used as a rinse. Hydrogen peroxide has potential side effects....Infected gums are from either gram negative anaerobic rod bacteria and/or from specific identifiable pathogens. Periodontal disease needs either biomechanical or surgical or biochemical intervention by dentist. Specific pathogens need identification & detox.

Gums: You are right. I would see a dentist as soon as possible for an evaluation and cleaning