Double vision would scare the crap out of me (as an adult), and a corneal ulcer is a big deal. I am sort of shocked at how laissez faire you seem to be and that this has been going on for a YEAR. Eye stuff can be terrifying and permanent.
If this were my child, I would be scheduling appointments with
another neuro-ophthalmologist (not the original unhelpful one) as soon as possible. What about the Wilmer Eye Institute at Johns Hopkins?
http://www.hopkinsmedicine.org/wilmer/services/neuro_ophthalmology.html Ranked one of the top eye hospitals in the country.