Hello,
While it isn’t unsafe to use a triple antibiotic ointment topically on a dog it is almost always not effective enough on its own to make much of a difference. If you have a wound or cut or laceration showing any signs of infection you need an oral antibiotic. I believe that almost all bite wounds get infected and an ointment isn’t adequate. Please see your vet if you are worried about infection or your pet has any signs of infection.