It's usually best to keep all your questions in the same thread so we don't keep asking for the same information...
Since I've already asked for your labs in your other thread, I won't ask for them here. That thread can be accessed via the following link:
I did ask in the other thread if the cause of your hypothyroidism had been determined... You should get tested for Hashimoto's, which is the most prevalent cause of hypothyroidism in the developed world. The tests you need are Thyroid Peroixdase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb)... You need them both, since some of us have one or the other and some have both. Elevated levels of either one can be the basis for a diagnosis of Hashimoto's, but either one can be present in small amounts in other autoimmune conditions as well.
Iodine is contraindicated with Hashimoto's as it can make the autoimmune response more intense... Your naturopathic doctor should have tested antibodies prior to suggesting iodine as a supplement.