Hi Eileen,
First, the thyroid disease and the eye disease are separate, with separate courses of disease and completely different treatments. Treating the thyroid does nothing for the eye symptoms. Doctors are beginning to speak of Graves’ as a "syndrome" rather than a "disease," so we have multiple issues to concern ourselves with. You’ve had your thyroid treated, so that part is mostly "done" except for monitoring and re-adjusting occasionally to allow for various things that bring on a need for different levels of thyroid hormone (age, weight, activity level, other hormonal "thresholds" like menopause).
Now, an RAI is supposed to kill your thyroid completely, so it renders you hypothyroid. HOWEVER, once you are taking thyroid hormone replacement and your blood levels of thyroid hormone and TSH are normal, you are no longer hypothyroid. You would be, if you stopped taking your thyroid hormone replacement, but as long as you are taking it and your levels are normal, you are NOT actively hypothyroid.
Are you under the care of an opthalmologist for your eye symptoms? That’s the right doctor for the job. It’s typical for Graves’ patients to have eyes that are very different (one sticks out more than the other, for example). If your eyes are actively changing right now (bulging more or less, giving you double vision, etc.), then usually a doctor will just wait and see, unless your vision is threatened (which is very rare). Still, it’s best to be under the care of a physician so you can more clearly define your transition into the "cold phase" when changes stop, because that is the time that you can start to talk about surgical solutions to the bulging.
I completely understand about the self esteem issues ~ some patients choose to use lightly tinted sunglasses all the time, which helps them "hide" their eyes a little. Anything you can do to help yourself feel better will help. I have heard that raising the head of your bed can help a little bit ~ I had a bit of "fat displacement" around my eyes because of Graves’, and sleeping with the head of the bed raised did help me. We put pieces of 4x4s under the bedframe. It’s better than using a stack of pillows because it keeps your head elevated no matter what (you can "come down" off the pillows while you’re sleeping) ~ plus with pillows you have a stress point at your hips that makes you uncomfortable over time.
In any event ~ there are things the opthalmologist can discuss with you for keeping the inflammation down as much as possible. The doctor could also give you some idea of the severity of your condition.