There are a number of different causes of hyperthyroidism so please be careful about the experience of individuals.
It is important that you see an endocrinologist to get a diagnosis. This may involve blood tests, imaging and or a fine needle aspirate where a tiny needle is put into the thyroid gland to take a sample.
The treatment will depend not only upon the diagnosis but also your age and occupation. It may involve drugs, irradiation, surgery or a combination, BUT without a face to face consultation with an endocrinologist this is pure speculation.
Your ability to regain a license unfortunately depends upon these findings as well as your regulator's rules, so sadly we cant tell you if or when you might be able to do this
Good luck