You don't necessarily need an Endo, just a good thyroid doctor. From the sources I know of for doctor recommendations I have none in Santa fe, but have two in the Albuquerque area. Sending you a PM with info. To access, just click on your name and then from your personal page, click on messages.
The Levo itself is not the cause for your symptoms. There are numerous processes and variables that affect your thyroid status. From the limited test data, your symptoms appear to be the result of Free T4 and Free T3 being too low in their ranges.
People sometimes think think it is the medication, but it is really the effect on TSH and natural thyroid hormone production, which results in little/no change in FT4 and FT3 levels until the TSH is essentially suppressed, and med dosage is further increased. There are scientific studies showing that hypo patients taking thyroid med adequate to relieve symptoms usually have suppressed TSH. Another contributor is that T4 meds are not adequately converted to T3 for many hypo patients. Many of us have found through experience that we needed Free T4 to be at least mid-range and Free T3 to be in the upper third of its range, and adjusted from there as needed to relieve symptoms.
So you really need to re-test Free T4, Free T3 and increase dosage of Levo. Also need to test cortisol to make sure it is sufficient. Also need to test Vitamin D B12 and ferritin and then supplement as needed to optimize. D should be at least 50 ng/mL, B12 in the upper end of its range, and ferritin should be at least 100.
If you live in the U.S. and find that you need a good thyroid doctor then if you will tell us your location, perhaps we can suggest one that has been recommended by other thyroid patients.
There were a number of thyroid related tests done that are outdated and not very useful: T3 uptake, Total T4, and Total T3. Right away that give me concerns about your doctor's knowledge of hypothyroidism. At any rate, your Thyroid Peroxidase antibodies test was very high, indicating primary hypothyroidism, due to Hashimoto's Thyroiditis. Usually this results in high TSH as the thyroid gland is attacked and eventually destroyed by the antibodies. Your TSH was only 1.25, which makes me wonder if there is a also dysfunction in your hypothalamus/pituitary system that is keeping the TSH low. So that is something you should ask the doctor about.
Looking at results for the biologically active thyroid hormones, your Free T4 was only at 22% of its range, and your Free T3 was at about 14% of its range, assuming that the Free T3 range listed is correct. I say that only because I have not seen such a range before.
In assessing a person's thyroid status, symptoms are always the most important consideration. You have several symptoms that are typical of hypothyroidism, and those are confirmed by your relatively low FT4 and FT3 levels.
So yes, it is directionally correct that you were started on thyroid med. The problem is that 62 mcg of T4 is not enough to relieve symptoms. I suggest that you should go back and get re-tested for Free T4 and Free T3. I am sure that you will need a substantial increase in your dosage. You also need to test for cortisol since it can adversely affect thyroid, so you need to be sure it is okay. Hypo patients are also frequently deficient in Vitamin D, B12 and ferritin, so you need to test those and then supplement as recommended in the link above. You also need to find out if the doctor is going to be willing to treat you clinically, as previously described, to relieve symptoms. If not, then you will need to either get him to read the info in the link and change his mind, or find a good thyroid doctor.
The first thing to understand is that the 62 mcg of Levothyroxine is not added to your thyroid hormone levels. When you start with thyroid med, your TSH goes down, and thus your output of natural thyroid hormone also is diminished. Since serum thyroid levels are the sum of both natural thyroid hormone and any thyroid med, that means that only when TSH is suppressed enough to no longer stimulate natural thyroid hormone production , will serum thyroid levels reflect further increases in thyroid medication.
I suspect that the doctor is medicating you just to get your TSH back within range, which doesn't usually work for the patient. A good thyroid doctor will treat clinically, by testing and adjusting the biologically active thyroid hormones, Free T4 and Free T3, as needed to relieve hypo symptoms, without being influenced by resultant TSH levels. So you need to find out what tests have been done, and then post results and reference ranges shown on the lab report so that we can help assess your status and advise further. If you haven't been tested for both Free T4 and Free T3 (not the same as Total T4 and Total T3), then you need to get those done. Also since hypothyroid patients are so frequently deficient in Vitamin D, B12 and ferritin those need to be tested as well. Can you get all this done?
If you want to confirm what I have told you I suggest reading at least the first two pages of the following link, and more, if you want to get into the discussion and scientific evidence for all that is recommended.
http://www.thyroiduk.org/tuk/TUK_PDFs/The%20Diagnosis%20and%20Treatment%20of%20Hypothyroidism%20%20August%202017%20%20Update.pdf
What is your daily dose of Levo? Please post your last set of thyroid related test results and reference ranges shown on the lab report.