Treat red patch of skin ourselves?

Dog has been chewing at her hindquarters lately and I noticed today it’s raw. Red, but no pus or other signs of advanced infection.

Rather than pay hundreds of dollars to have her seen, can I try a first course of antibiotics myself and watch a few days for either a) improvement, or b) worsening? If it gets worse, we’d book a vet visit.

Most antibiotic ointments (eg Animax) require a Rx, but Sulfodene does not. Would it be unwise to give it a shot myself first? If there’s no change after a few days, I’d continue treatment for a week before reevaluating.