Peroxide acts as an antibacterial by introducing free radicals in the form of a single O (oxygen) ion to bacteria which don't have oxidase to neutralize it like we do. That's why it's also used as a mouthwash. Alcohol works by denaturing proteins in the cell wall of bacteria and dissolving lipids which goofs the bacteria up big time. Both are fine to use. But yeah, I'd probably go to the doctor if you've got pus oozing out and it hurts.