Benzoyl Peroxides are excellent for treating acne. They kill the non-pathogenic, but troublesome bacteria, P. Acnes, in a clever way. As students of this kind of thing know, P. Acnes florishes in an anaerobic or micro-aerobic ( non-oxygen containing) environment. Through peroxidation, BP percolates tons of oxygen molecules, thus basically smothering the P. Acnes bacteria. Since this process does not utilize mechanisms such as blocking bacterial ribosomes, or damaging cell walls etc. the bacteria cannot develop resistance, plasmids and such do them no good here. They die.
Not only does BP kill bacteria, but it does some desquamation (peeling) as well. This helps open up the clogged pores, a key component of the acne problem.
As good as Benzoyl Peroxide is for acne patients, (and the makers of the greatly over-hyped and over-priced Pro-Activ), there are a number of acne-sufferers who are irritated by it. Further, a significant number of others either began with an allergy or have developed it while on Benzoyl Peroxide.
From your description, you most likely have either an irritant or allergic contact dermatitis. It would be important to avoid BP-containing products in the future. There are a number of effective topical medications besides BP. Your dermatologist can find one which would be a good fit for your skin problem and type of skin.