"Mouth Rot" aka infectious stomatitis is a disease of reptiles and can be caused by bacteria, viruses, and fungal infections.
The treatment described in the link Jen provided above is a treatment for reptiles and not amphibians. Iodine is toxic to amphibians and many of the iodine solutions also contain surfactants which are also toxic to amphibians.
The swelling looks to be localized and can be caused by a number of issues and really needs to be evaluated by a vet.
Ed