I get the idea that your doctor is medicating you based on TSH only. that is just wrong. TSH is a pituitary hormone that is affected by so many variables that at best it is only an indicator, to be considered along with more important indicators such as symptoms, and also levels of the biologically active thyroid hormones, Free T3 and Free T4 (not the same as Total T3 and T4). After starting on thyroid meds, TSH is almost useless as a diagnostic by which to determine med dosage.
If my assumption is correct about TSH being the only test being used to treat you, then you should insist on being tested for Free T3 and Free T4 each time you go in for more tests. Also, since Hashimoto's Thyroiditis is the most common cause of diagnosed hypothyroidism, you should also request to be tested for the thyroid antibodies associated with Hashi's. those tests are TPO ab and TG ab. Those tests would rule in or out the possibility of Hashi's. Since hypo patients are also frequently deficient in other areas, you should make sure to be tested for Vitamin D, B12 and ferritin.
When you have those test results, please post them along with reference ranges and members will be glad to help interpret and advise further.
It seems a little strange to me that your doctor took you off Synthroid after a few months. Usually, once you start taking it you are on it for life. The doctor should definitely put you back on the meds and keep you on it (unless there is a good reason to take you off). Once your thyroid levels are in the normal range you should be fine but you should expect to be taking these meds for the rest of your life and have bloodwork done periodically (probably once or twice a year).
I have been on Synthroid for over 2 years and have no side effects from the drugs. I've only had to increase the dosage once so far.
Laura