Using Iodine for inactive thyroid

I am a 55 yr old woman with inactive thyroid but takes thryoid meds/saw in a few articles that I should be taking 5 mg a day of Iodine? My hair is terrible, my skin feels terrible, I don't sleep, I am gaining weight even though I am weight watchers, I am tired, all the same symptoms as I had before the meds. My Dr does not seem to believe in supplements except D. I had a deficiency in vitamin D and I take 1000 mg per day. Will Iodine have side effects? I had an image done of my thyroid and it is the size of a pea. Feel terrible and should not. Help!!!