Don't take this as a recommendation, but I've been to an ophthalmologist a couple of times in Chetumal, and I'm satisfied with him.
In the building where he's located, there's a place selling eyeglasses, but I've never been in that part (I don't wear glasses), so don't know if there's an opometrist employed there, or if the ophthalmologist also works as an optometrist.
Both businesses share the same entrance from the street.
Dr. Mario Alberto Briceno Navarrete
Centro Oftalmologico de Chetumal
116 Av. Juarez (from memory, it's at the corner with Calle Lazaro Cardenas).
Av. Juarez runs parallel to Av. Heroes, one avenue west of Heroes.
Open M-F 08:30 to 13:00 and 17:00 to 20:30 and Saturday mornings.