Hypothyroidism is not just caused by inadequate thyroid hormone. The correct definition is "insufficient T3 effect in tissue throughout the body due to inadequate supply of, or response to, thyroid hormone". Your current Free T4 level is more than adequate but you don't know what your Free T3 level is, so you cannot know if your T4 med dosage is being adequately converted to T3. Also, most hypothyroid patients taking thyroid medication adequate to relieve symptoms, such as hair loss, find that their TSH becomes suppressed below range. Your TSH is still high at 8.7. In addition, hypothyroid patients are frequently deficient in Vitamin D, B12 and ferritin, so you need to get those tested 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. Each of these affects the tissue response to thyroid hormone. Ferritin is also important for good hair growth.
So you need to get tested for Free T3, and if not already done, then also Vitamin D, B12 and ferritin. Also note that you should not take your thyroid med until after the blood draw for thyroid tests, in order to avoid false high results. If you can you get these done and then post results and their reference ranges shown on the lab report, we will be happy to help interpret and advise further. Also, if it turns out as I expect that your Free T3 is too low, will your doctor be willing to add a source of T3 to your medication?