When I had braces my orthodontist had me swish a 50/50 mix of hydrogen peroxide and mouthwash to clean every little place I couldn't get with my toothbrush and I had beautiful white teeth.
Hydrogen bubbles when it comes in contact with germs. Your mouth is full of bacteria to aid in digestion, so it foams. Whenever I have a gum problem I swish with a 50/50 mixture of peroxide and mouthwash and it always clears it up, plus it whitens your teeth.
Hydrogen peroxide is the main ingredient of MOST teeth-whitening systems so if you have a sensitivity to one, you probably will to the other. But it does work really well, for me at least.
PS. I've used hydrogen peroxide on an infected ingrown toenail and it was the ONLY thing that could get in and clear up the infection and keep it away.