Your doctor missed maybe the most important thyroid hormone test, which is Free T3. Free T3 is used by cells throughout the body, and it correlates best with hypothyroid symptoms. The Free Thyroxine Index and T3 Uptake are .outdated and not very useful. Instead of the Total T4 test it would be much better to test for Free T4. So far your doctor doesn't impress with his thyroid knowledge.
From the little useful test data, your TSH is high, and should be followed up with tests to check for the presence of antibodies from Hashimoto's Thyroiditis. A test for Thyroid Peroxidase antibodies should be done first, and if negative, then a second test for Thyroglobulin antibodies should be run. Those tests are often listed as TPO ab and TG ab. With Hashi's there is a dysfunction in the hypothalamus/pituitary system with which the thyroid gland is identified as foreign to the body and antibodies are produced to attack and over an extended period the gland is destroyed. As this proceeds, the output of thyroid hormone is diminished and must be replaced with thyroid medication.
So you need to find a good thyroid doctor that will treat you clinically by testing and adjusting Free T4 and Free T3 with thyroid medication as needed to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results, and especially not TSH when you are taking thyroid med. Such a doctor will test for TPO ab, TG ab if needed to confirm Hashi's. Also will test for Free T4, and Free T3. Hypo patients are frequently low in other areas as well, with the most frequent being Vitamin D, B12 and ferritin. So you need to get those tested and supplement as needed to optimize. D should be 55 min., B12 in the upper end of its range, and ferritin should be 70 minimum.
When did the doctor start you on the 137 mcg of Levothyroxine?
The 137 mcg is a hefty dose to start on. T4 meds build up somewhat slowly due their half life being about one week. That means that it will take a week for the dose to build up to 50 % of its final effect on serum levels. So it takes about 4 weeks to see over 90% of the final effect on serum levels.
When are you scheduled to return for followup tests?
What all of us here look for and need is a good thyroid doctor, as I described above. That does not necessarily mean an Endo. They seem to be less likely to treat clinically, as described, than other doctors. If interested I have a couple of names of doctors in your area that have been recommended by other thyroid patients.
Be sure to ask for Free T4, along with the Free T3, instead of Free T4 index. FTI is a round about way of calculating FT4, when the actual FT4 test is much more accurate. Judging from the tests he's ordering, your doctor is a bit behind the times.
I just sent a PM with info. To access, just click on your name and then from your personal page, click on messages.