The tests you should request are Free T3, Free T4 (not the same as Total T3 and T4), TSH, Vitamin D, B12, ferritin, and
a full iron
test panel. If the doctor resists, just insist on these and don't take no for an answer. They are all important. One last thing here, if the cause for your being hypo was never determined, then you should ask to be tested for the thyroid antibodies associated with Hashimoto's Thyroiditis, which is the most common cause for diagnosed hypothyroidism.