I had graves disease some years ago. Had to have beta blockers, carbimazole (to block the thyroid) and thyroxine. The beta blockers were stopped as soon as the condition was under control. The block replace therapy carried on whilst they tried to stabalise it. For me this went on for over 6 years. In the end I had to have the whole of my thyroid removed and just take thyroxine now.
My advice would be don't have any radioactive therapy - regardless of what anyone says.