Does my skin look damaged?

I’ve had a pimple that has been on my face for over a month and it wouldn’t go away so my dermatologist prescribed me clindamycin with benzoyl peroxide. I’ve never used it before or any acne topicals before but I have it a try for the first time yesterday’s do it immediately got rid of the pus in the pimple that wouldn’t come out, so it worked great on my first day. I applied it again this morning on two of my pimples, and the skin where I applied the cream got red and the redness won’t go away. The skin around and underneath looks like it’s been damaged on the outer layer around the pimples. I’m really worried it’s damaged my skin and made it now look Worse than what I was dealing with before.