With all those symptoms you obviously want to get your thyroid hormone levels optimized as soon as possible. Since you started on the 100 mcg of T4 med in August, it will be at over 90% of its full effect in 4 weeks, so a re-test in that time could have shown the need for an increase in your meds sooner.
When you go back for re-test, it is very important that you are tested for both Free T4 and Free T3. Insist on both and even go so far as to quiz the lab person to make sure they know you are to be tested for both Free T4 and Free T3. Otherwise you sometimes don't end up with what you need.
Since hypothyroid patients are so often deficient in Vitamin D, B12 and ferritin, I also highly recommend getting those done as well and then supplementing as needed to optimize. D should be at least 50, B12 in the upper end of its range, and ferritin should be at least 70.
A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results. So I recommend that you ask your doctor if he is willing to treat clinically as described. If not then you will ultimately need to find a good thyroid doctor that will do so.
You can get some good info that will best prepare you for your doctor appointments by reading at least the first two pages of the following link, and further if you want to review the discussion and the scientific evidence supporting the suggestions on page 2.