I have Hashimoto's and iodine is most often contraindicated for those of us with Hashi's; it can cause much more harm than good. Once antibodies have destroyed thyroid tissue, nothing will restore that tissue; it's gone forever.
Many of us have to wrangle with our doctors to get proper testing/treatment. I'm struggling with mine right now, because my FT3 and FT4 levels are too low and he won't give me an increase, due to my low TSH.
I was diagnosed with graves disease over 20 years ago and have had to wrangle with more than one physician to basically treat myself. Do you have a puffy chin area or a double chin? Iodine is food for your thyroid and can have unbelievable results. When I started taking organic iodine, I felt like a new person. You should feel within a week of starting, if its going to work for you. Its cheap and lasts a long time. Iodine is kindof like iron in that you can build up your reserves and then discontine for a while. My body would signal when to restart iodine. I could feel the tenderness under my chin, I had pseborea to die for, and that lack of restful sleep.
I commented on the other thread you started. The symptoms you noted: fatigued, sleepy, anxious, nervous and palps can apply to either Hashi's or Graves.
You didn't post any labs that indicate you have Graves Disease. As I noted on that thread, it's very common for people with Hashi's to swing hyper to hypo and back. Your actual thyroid hormones, indicate hypo.
TSH is so variable, it can't be used, alone as a diagnostic or to determine dosage. My TSH stays at < 0.001, I have those same symptoms, at times, and I'm hypo.
I think it will be easier for everyone to keep up with your situation, if we stick with just one thread vs back and forth on 2 threads.