I wouldn't use hydrogen peroxide on the chin because it is drying and will irritate the skin further. You can get a special cleanser from the vet or simply use a wash cloth with warm water. The main parts to clearing up the chin acne are: cleaning the mouth and chin area twice a day; gently scrubbing the chin to rev up blood circulation in the area; and don't use plastic bowls.

I once had 7 cats with chin acne at the same time and thought I would go mad. But it did clear up eventually and I've stuck with ceramic and glass bowls every since, one day of use and into the dish-washer which has a final sterilize function.