First, the doctor should be testing for the biologically active thyroid hormones, Free T4 and Free T3 (not Total T3) every time you are tested.
Your Free T4 is adequate. Your Total T3 is only about 38% of its range. If your Free T3 is similar in range, then that is a likely contributor to your symptoms. 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. I say that about TSH because hypothyroid patients taking thyroid med frequently find that their TSH becomes suppressed when taking adequate thyroid med. Your TSH is far from being suppressed and TSH should not be a consideration when medicating a hypothyroid patient. So you need to get tested for Free T3 and get your med dosage adjusted as needed to relieve symptoms. Many of us have found that we needed Free T4 at least at mid-range, and Free T3 in the upper third of its range, and adjusted from there as needed to relieve symptoms.
You can read about all this in the following link. I highly recommend reading at least the first two pages, and more, if you want to get into the discussion and scientific evidence for all that is recommended.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
In addition, hypothyroid patients are frequently deficient in Vitamin D, B12 and ferritin, so it would be good 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.
A combination of all of the results
On what basis is the doctor adjusting your meds? Is it based on the TSH level?