Thanks all, here's an update: went to the vet today, and he was much calmer than the first time we brought him- didn't try to chew the vet's hand off.

Vet doesn't think it's melanoma because it isn't raised up, and melanoma usually concentrates on one, not multiple spots in the eye. We have to just watch it to make sure nothing changes. Got his rabies shot and let out one little mew, but he was really good, and is healthy (but a little fat :3).