It's unfortunate that your doctor is relying so heavily on TSH and not even on Free T4... It's customary to maintain suppressed TSH following thyroid cancer, however, your Free T4 is on the high side.
Have you had a Free T3 test? Free T3 is the active hormone that's used by individual cells in the body.
Having high thyroid hormone levels can cause fatigue, but so can other things, such as low vitamin B-12, low ferritin, vitamin D, etc.
If you haven't had those things tested, I suggest you get them if possible. If your doctor won't order them, it may be time for a new doctor.
I neglected to mention that my tsh of .07 was .35-3.30 standard range ulU/mL and my free T4 of 1.61 was .56-1.64 ng/dl standard range.