Have you ever checked your Basal Body Temperature (BBT) by taking your temp first thing in the morning before getting out of bed? As arcane as it sounds, it is far more accurate to determine thyroid function than any of the 'advanced' tests the doctors are using.
Synthroid and Levothyroxine are anti-thyroid medications. I don't know how much you have been educated by your doctor about the function of the thyroid gland and its hormones, but both of those drugs are T4 analogs and T4 must be converted to T3 in the cells in order to increase cellular metabolism. These drugs feedback to the thyroid and shut off production of TSH and don't actually even work at the site where the problem may even lie (in the individual cells).
Additionally, there are 'reverse T3' & 'reverse T4' molecules that competitively inhibit the functioning of T3 & T4, and I don't know of a single doctor that checks these.
Broda Barnes was an MD that studied the thyroid gland for 52 years during his career. I would look him up. He would use thyroid glandulars. I used to think iodoral was a good idea, but have seen too many people react too strongly to it. There is a large release of Bromine into the system that causes many problems. The glandulars provide Iodine
as well as T3 & T4 and nutrition for the thyroid gland itself. To determine the proper does, you must use your BBT and calibrate the dose, building up to the point that your BBT is in the proper range.
There are also herbs that can help increase your thyroid function. PM me if you have any questions.