I know of no eye doctor on AC. There is one in Belize City.
Don't assume things are cheaper here, necessarily. Sometimes going to a medical practitioner here can be about the same as the States. It's kinda a pay what you can afford thing, and it is often assumed that gringos can afford to pay more. So, gringos are charged more. That isn't a bad thing either, as local Belizeans who might not be able to afford much, can get medical care. Think of the "sliding scale" of your local community run clinic.