Over the years I remember hearing about alcohol, mercurochrome (if you like your skin a nice shade of red), hydrogen peroxide, Bactine (an ammonium salt), etc.
However, I can't use any of the common topical antibiotics. Not even bacitracin alone. My wounds only get worse when I use it. I learned from a dermatologist that the best treatment is just plain petroleum jelly. The body is pretty good at fighting infection and the main thing with petroleum jelly is that it keeps the wound area moist and protects against other things getting in. Doesn't really have to be sterile either. It will reduce scarring by preventing scabs from forming. Maybe there are specific reasons for using an antibiotic or other antimicrobials under a doctor's care, but for most light wounds the best thing to do is to clean it and then apply petroleum jelly.
2. Help injured skin heal. For minor wounds such as cuts, scrapes, and scratches, use petroleum jelly to keep the wound moist. This helps prevent the wound from drying out and forming a scab, as scabs take longer to heal. This will also help prevent a scar from getting too large, deep or itchy. As long as the wound is cleaned daily, it is not necessary to use anti-bacterial ointments.
The first time I figure out that I was allergic to one particular antibiotic, a nurse practitioner prescribed a corticosteroid ointment. It had been inflamed for weeks and I couldn't figure out why since Polysporin was supposed to be free of neomycin. But after applying the corticosteroid, all the weeping was gone overnight because it tends to dry things out and the inflammation was gone. Within two days I had dead skin just completely peel off. I could see a mild scarring, but it was almost perfectly smooth.