See a doctor for your inquiry about hormonal related acne.
Hydrogen peroxide is a peroxide with the empirical formula, H2O2. This makes it an extremely effective oxidizer, just like anything in the peroxide category.
When your skin whitens after topically applying hydrogen peroxide that is from the oxidative nature and its referred to as an oxidized capillary embolism.
The bacteria that is known to cause acne, propionibacterium acnes (P. acnes) is an anaerobic bacteria and introducing an oxidative environment destroys the bacteria. (with air-aerobic/without air-anaerobic)
My suggestion? Try to switch over to benzoyl peroxide vs. the more harsh hydrogen peroxide. If you just want to use topical compounds then you should check out Witch Hazel. Its a lot less harsh, also an antiseptic/antibacterium/antimicrobial, and its even an astrigent!