I agree that a second opinion is the best first step.
Good question about the iodide recommendation. Normally, iodide would be a good idea with low TSH levels. Perhaps you should ask the doctor for a more detailed explanation. Otherwise, you may find help with the question at the Iodine Supplementation forum.
Not saying that this may be the case with your doc, but some docs are fairly clueless when it comes to iodide/iodine.