Unless your doctor is really gung-ho about it/you have really good insurance, I wouldn't get my thyroid tested. Thyroid problems tend to cause systemic problems, like weight gain, cold intolerance, slow heart rate, depression, thin fingernails, thinning of the outer third of the eyebrows, and a whole host of other symptoms, so I doubt that you have thyroid issues if your eyes are the only thing bothering you.