I think doing the antibiotics is the right thing to do.. But putting betadine ON it won't do any good.. You need to rinse the abcess out With the sterile water OR with a betadine solution. People do it all the time for dogs and horses, and cats.
You can look online to find a mixture solution. In the mean time I would seriously go to a feed store OR go to a vet and by a syringe and needle and go in there and get that puss out and open that abcess up. And rinse it with sterile water. YOu can spray the inside with a bacitracin/water mixture, it can't hurt. He probably won't like it..
But you have to get it OPEN and drain it.. the betadine won't do anything on the surface it needs to in where its infected.

Pleas keep us updated.

Carol