There are many different medical problems that could be associated with the thyroid gland. Most can not be cured "completely". There are not prescribed medicines nor homeopathic medicines that will "cure" you. That is like asking for a cure for diabetes. There is no "cure" but there are many things you can do each day to help you maintain healthy thyroid functioning. Talk to your doctor. He/She may prescribe a drug called "Synthroid" or something similar. (Note: some people cant eat soy products when taking synthroid. they get a weird, itchy, full body rash. It wont kill you, but will be very uncomfortable.)
I also love the curative effects of yoga (for almost anything!), but yoga alone is not going to do it. Kelp or nori and eating more fish might help, too. But the most important thing is to talk to your doctor, because a thyroid problem is not something that you should take lightly.