chafing

The red part you would call a 'rash' or a 'chafe'. In your case because it was caused by rubbing, a 'chafe' is the exact term, but a 'rash' is a more general term than many use. The difference between a 'chafe' and a 'rash' is a 'chafe' is always caused by rubbing or friction by something. A 'rash' can be caused by that too, but as well it can be be caused by allergies, infections and other causes. It is a more general term.

Chafing isn’t usually itchy. If your thighs are red and itchy, you might say “I have a rash on my thighs. It itches.” If your thighs are red and painful due to rubbing, you might say My thighs are chafed. I have chafed thighs from riding a bike. They hurt.