TSH is not an active thyroid hormone, it is a pituitary hormone that causes no symptoms. The biologically active thyroid hormones are Free T3 and Free T4. FT3 is the most important because it largely regulates metabolism and many other body functions. Scientific studies have shown that Free T3 correlates best with hypo symptoms, while Ft4 and TSH correlated very poorly.
Frequently patients taking large dosages of T4 meds do not adequately convert the T4 to T3, leaving them with a FT3 that is too low in the reference range. The reference range is far too broad, so members frequently report having FT3 in the low end of the range, yet they have hypo symptoms. Members also frequently report that symptom relief for them required that FT3 was adjusted into the upper part of its range and fT4 adjusted to around the midpoint of its range.
I expect that with your doctor's focus on TSH, you may not even have been tested for FT4, and certainly not for FT3. So that should be your first order of business, to get that testing done every time you go in to the doctor.
A good thyroid doctor will treat a hypo patient clinically by testing and adjusting FT3 and FT4 as necessary to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results. If you want to read more about clinical treatment, this is a link to a letter written by a good thyroid doctor of patients that he consults with from a distance. The letter is sent to the patient's primary doctor, to help guide treatment.
http://hormonerestoration.com/files/ThyroidPMD.pdf
TSH reference range for above is .47 - 5.01