Watering eyes can be one of the most mis-understood effects we have. Infection and allergies are the two most likely non-diagnoses, because red, watery, itchy eyes look just like both of those. The doctors that are usually best at diagnosing this are Neuro-ophthalmologists. If necessary, a CT scan can show enlarged muscles.
I would really be asking my doctor. If both the anti-thyroid medications are out of reach for you, will be investigating another treatment.