Because your TSH is almost 2, I can tell you're being undertreated. It's much more common than you'd ever believe. But it isn't surprising that an MD who would use such outdated, useless tests would not be prescribing you as much hormone as you need.
You must insist on tests for blood levels of free T4 and free T3. The free T4 index you had is worthless. (There are no tests currently for T1 or T2 levels. That doesn't mean these hormones aren't important; they're just produced in amounts too small to measure. If you could get your MD to switch you to natural dessicated thyroid hormone from Synthroid, you would get the T1 and T2, along with T4/T3, that your Synthroid does not provide. I'm pretty sure he would never allow you to do that though - See paragraph 1.
You may have to find another MD to get the right kind of thyroid replacement that will restore your health.