Ask for a copy of your lab results and check to see if the dr. tested for antibodies. My dr tested me and did an ultrasound because I had all the symptoms. Only the antibodies showed that something was wrong.
Just ask him the results, ask him the TSH, because new range (American) is between 0.3 and 3, but for most doctors normal range is between 0,3 - 5.
Your tests showed a TSH above 4.0.
Your problem is the Endo, not the tests.
Ask to have the thyroid tsets run again, and if the doctor objects, tell the doctor that 4.0 is high, and a Free T4 of 0.9 could be considered a little low, and you'd like them done again along with a Free T3.
When the new tests come back, if the docotr doesn't want to medicate, then ask if any other tests might reveal a way to improve the function of the gland. You may be low on iodine or selenium or other things that facilitate production and conversion of the hormones.
Always ask for a copy of your lab results. It is your right. Some drs haven't accepted the new levels in place now. Have you researched (which I am pretty sure you have) thyroid nodules+normal lab values?
Another thought, sometimes a GP will work better with you than an endo.