I recently watched a summit on thyroid and adrenals, which are intimately connected, along with the liver and one's gut health. (The entire endocrine system really.) We need them all to be working correctly and healthy to get any real lasting results.
So much information. Your best bet is to find either a Functional doctor, a Naturopathic doctor, or even better, one that is integrative.
Your thyroid needs selenium, iodine, zinc, tyrosine, but you also need to attend to adrenals, liver, and gut health to have an impact. Adrenals need a healthy dose of Vitamin C. Liver needs to work well as that is where the T4 is converted to the T3 that the thyroid needs. It's a complicated process that involves more than just the thyroid.
.OH. And something VERY Important I learned a only couple months ago: DO NOT EAT ANYTHING WITH GLUTEN in it. Evidently the thyroid sees gluten as another substance that it needs to attack which inflames it.