What do you mean by "puffy"? Is there a bump under the skin? Difficulty eating and "puffy" area makes me think of an abscess caused by an overgrown/infected tooth, we need a better description. They can also itch as a response to pain.
Is the skin dry and red? Is there any way you can post a picture?
It could also be fungal, they can catch this from others that are infected. Though, fungus wouldn't really cause difficulty eating.
Regardless, he needs to be seen by a vet.
The price of exotics vets depend on the individual vet and the area in which you are located. Every vet's exam fee is different, and the diagnostics range in prices as well.