Can the wrong eye glass prescription cause a 3 year old eyes to get worse if he is diagnosed as having amblyopia?

Yes. Having the right prescription is very important in the treatment of amblyopia. While there are several causes, the pathway is the same: the brain suppresses the vision in the weak or non dominant eye leading to progressive loss of vision from nonuse. Treatment other than lenses may be necessary. Be sure he is being treated by an expert pediatric ophthalmologist.