If you don't have an extremely accurate graham scale or a vet to tell you dosage (or experience doing it yourself) you want to stay away from that stuff. Antibiotics can do more harm than good if you get dosing wrong. If you can contact a vet and order some based on their recommendations it'd be a good idea though.
He's looking a lot better!
Rafacacho is right that there's bacteria in the whole body. But if you continue to treat the oral symptoms and he can eat, drink, and otherwise be healthy, eventually the idea is that he'll knock the infection. If they can't eat or drink they can't fight it off. This is why vets are ideal for this type infection, but I get that that isn't always possible.