Where should I go if I have diplopia?

See strabismologist. Diplopia, or double vision, usually occurs from misalignment of the two eyes. This can be due to eye muscle imbalance and other factors. A motility specialist, or strabismologist can assess the situation and come up with a treatment plan. Glasses with prism may help or surgery.
Ophthalmologist. If of recent onset, then an ophthalmologist should be consulted (not an optometrist). The cause may be found there or you might be referred to a neuro-ophthalmologist or to a neurologist. Diplopia usually results from pathology that needs diagnosis and treatment. Do not ignore this.