Peroxide doesn't sound like what you need, but it certainly can't cause permanent damage. It sounds to me as though you have irritation rather than infection. I advise you to try 1% hydrocortisone
twiceTwice-a-day a day for a few days and stay away from peroxide there. You should also consult a dermatologist about dealing with cracked skin in that area. But you don't need to worry that you damaged yourself.
Best.
Dr. Rockoff