In my opinion a good thyroid doctor will treat you clinically by testing
and adjusting levels of the biologically active
thyroid hormones, free T3
and free T4 (not total T3 and total T4), with meds as necessary to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief is all important, not test results.
FT3 and FT4 tests results are best used as markers to measure your increased levels as you progress toward symptom relief.