From your tests you apparently have Hashimoto's Thyroiditis, which is the most common cause for diagnosed hypothyroidism. Hashi's is caused by the autoimmune system erroneously tagging the thyroid gland as foreign to the body and producing antibodies to attack and eventually destroy the gland. As this proceeds, typically the output of thyroid hormone is gradually reduced and the TSH rises, requiring thyroid med to relieve symptoms.
Since you are taking thyroid med your Free T4, at about 65%, is good and your Free T3 is at 76% of its range, which is a level that is frequently adequate for relieving hypo symptoms. So this points to the need to test for other possibilities.
You seem to be adequately converting the T4 med To T3, so I would not bother testing for Reverse T3. Hypo patients are frequently too low in the ranges for Vitamin D, B12 and ferritin, so I would get those tested and supplement as needed to optimize. D should be 55-60 mi. and B12 in the upper end of its range, and ferritin should be 70 min. Low D and low ferritin can adversely affect metabolism of thyroid hormone. .
You said you feel ill all the time. Please describe more specifically what that means. Also, what dosage of T4 are you taking?
Thank you for your response.
T3 4.7 Range: 2.8-5.3
T4 1.7 Range 0.8-2.2
Just being anywhere within the so-called "normal" ranges may not be adequate. Please post the actual T4 and T3 test results and reference ranges shown on the lab report.