Hi Diane, I have heard about three places in Belize City that might be able to help:
Hoy Eye Center – http://www.hoyeyecenter.bz/
BCVI Eye Clinic – https://www.bcvi.org/
And you already reached out to the below, but sometimes in Belize calling is the only way to get a hold of people. It is somewhat like the 1950’s here, still!
BELIZE VISION CENTER – try calling them at 011-501-224-5038
If you do not find the resources you need, another option is to check out Chetumal or Merida, Mexico, which are close enough by that expats often go there for medical care, and it is a quick flight or ADO bus away! Hope that helps,
Laura