There is no way I can tell from the information you provided and without and examination. There is no reason to disbelieve what you were told especially if this is a strabismus Eye MD.
JCH MD
I saw a strabismus opthalmologist. He told me to do rolling,focusing, and tracking exercises with my eyes.He told me these exercise will help my brain to use my eyes together.Ask him about surgery and he say it will only makes your eyes straight for about 5-10 yrs and i may need another surgery. So he told me wear prescription eye galsses with a balance prescription.He told me that eyeglasses will keep my eyes from strain. How long would it take my eyes to work together and he told me about a year. Is this is a true statement.
The glasses will have no affect on the position of your eyes nor your amblyopia. As an adult neither amblyopia or exotrophia can be cure with glasses. Glasses may make you see better but amblypia means vision that does not improve with glasses. Get a second opinion from a strabismus-pediatric ophthalmologist.
JCH MD