In my opinion you should try to allocate a little bit more time between immediately cleaning the surface of your face and then applying benzoyl peroxide. It's a compound within the same biochemical classification as the popular hydrogen peroxide. They both have very intense oxidative properties resulting very aggressive exfoliating abilities as well as antiseptic, antibacterial, antifungal. Really just to keep this simple almost every form of anaerobic bacteria that is predominantly associated with blemishes cannot survive the rapid onset of oxidative stress.
It is possible to put too much on your skin though and cause some acute oxidative damage to your hypersensitive skin cells below the previously exfoliated layer. The damage if you don't blatantly continue with the application is temporary, but I don't know anyone that tried to go further. I

would say that the extreme redness along with the localized irritation and itching is because the skin that is currently exposed is newly developed, lacks the sufficient integrity due to the premature exposure with less keratin than normal, and the oxidative stress increasing it's likelihood to become over reactive to any form of outside contract.