Sia has Graves' disease too, so you're in good company. I had a slightly underactive thyroid before I started HRT. I was prescribed some kind of thyroid drug to take indefinitely. "To hell with that," I proclaimed! Instead, I picked up some thyroid supplement at the health food store and took it for the duration of the bottle. My thyroid problem cleared right up, and I didn't need the drug. To this day, my thyroid is fine.
Keep in mind, while I had great success with some herbal thyroid treatment, my thyroid was only slightly underactive. If you had to basically destroy yours to halt Graves' disease, then you might be in a very different boat. Always, always, ALWAYS talk to your doctor! (yes, I totally get the irony here)