The thing you need most is a good thyroid doctor. By that I mean one that will treat a hypo patient clinically by testing and adjusting Free T3 and Free T4 as necessary to relieve hypo symptoms, without being constrained by resultant TSH levels. You can gain some valuable insight from this link written by a good thyroid doctor.
http://www.hormonerestoration.com/Thyroid.html
TSH is a pituitary hormone that is supposed to accurately reflect levels of the biologically active thyroid hormones Free T3 and Free T4. In reality TSH cannot be shown to correlate well with either Free T3 or Free T4, much less correlate with symptoms, which should be the foremost consideration.
Further, your current doctor fails to understand that after starting on thyroid med, TSH is frequently suppressed below range. That does not mean that you are hyperthyroid and need to reduce meds. You are hyper only if having hyper symptoms due to excessive levels of Free T3 and Free T4 which you do not have. Without knowing the specific ranges for your tests, I expect that your Free T4 is about mid-range, which is adequate; however, I'm confident that your Free T3 is too low in the range. That is a frequent occurrence when taking only T4 meds. The body frequently does not adequately convert the T4 to T3. Scientific studies have shown that Free T3 correlated best with hypo symptoms, while Free T4 and TSH did not correlate at all.
So, you need to find a good thyroid doctor that will treat clinically as described. If you will tell us your location perhaps we can suggest a doctor for you.
Last for now, since hypo patients are frequently too low in the ranges for Vitamin D, B12 and ferritin, if not already tested that needs to be done. If tested previously, please post results and ranges shown on the lab report.