In trying to assess the thyroid status, the most important consideration is symptoms, followed by the biologically active thyroid hormones, Free T4 and Free T3. You have mentioned several symptoms that are frequently related to being hypothyroid. Your Free T4 is way too low, even below range. You should always make sure they test you for Free T3, not Total T3 in the future. Free T3 is way more revealing than Total T3. If your Free T3 is similar to your Total T3, then that would be extremely low, and another indicator of hypothyroidism.
If your doctor did not react to your symptoms and those lab results, and offer a prescription for thyroid medication, then the doc is apparently only interested in TSH, and you will need to find a good thyroid doctor. A good thyroid doctor will treat a hypothyroid patient clinically, by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms. without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results, and especially not TSH. Many of us have found that Free T4 needed to be at least mid-range, and free T3 in the upper third of the range, and adjusted from there as needed to relieve symptoms.
In addition, Vitamin D, B12 and ferritin are very important for a hypothyroid patient. Your Vitamin D is way too low, since it should be at least 50 nm/mL. B12 is excessive. It should be in the upper part of the range. If supplementing, you should cut back. Your ferritin is terribly low, since it needs to be at least 100. Having adequate thyroid hormone levels, along with adequate ferritin levels are very important for good hair growth. So you need to supplement your Vitamin D and ferritin as needed to optimize. I expect that you will need about 3000 IU daily of D3, and at least about 65-75 mg of a good iron supplement like VitronC. Other good iron supplements are iron fumarate, iron bisglycinate, and iron sulfate. These will need to be taken with some Vitamin C to help avoid stomach distress from the iron.
Most important for you is to find a good thyroid doctor that will treat clinically, as described above.