I know that Bill is far more experienced with frogs than I however I have been in rescue for years.

I personally would recommend contacting your local vet. Vets usually have a list of local rescues and may be able to help you locate someone experienced with frogs. If that fails here is a couple links that may be able to help.

Wild life rescue by state;

The Wildlife Rehabilitation Information Directory

Mississippi Wildlife Rehabilitation List of Mississippi Rehabilitators

Burns are one of the more serious injuries and most vulnerable to infection.
Good that you used an antibiotic ointment ( hope it did not have a pain killer very toxic to frogs) That is the main reason I would not release him. It could be a long painful death.
Great you cared enough to take the time to help the poor little guy,above and beyond even for a dog rescuer