I meant to clarify that no one here is a doctor. We are all just basically long time thyroid patients ourselves, who have spent a lot of time learning everything we can about hypothyroidism, so that we can pass it on to other members.
TSH is a pituitary hormone, not a thyroid hormone. TSH has been shown to vary as much as 70% over the full day. TSH does not correlate well with the actual biologically active thyroid hormones Free T4 and Free T3, and has no useful correlation with symptoms, which are a patients's main concern. TSH is affected by so many things that at best it is only an indicator to be considered along with more important indicators such as symptoms, and also levels of Free T4 and Free T3. TSH should never be used to determine thyroid medication dosage.
Instead, a good thyroid doctor will test and adjust Free T4 and Free T3 as needed to relieve hypo symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results.
So please tell us about symptoms you had when diagnosed as hypothyroid. Along with the high TSH were you tested for the possibility of Hashimoto's Thyroiditis being the cause? Those tests are Thyroid Peroxidase antibodies (TPO ab) and Thyroglobulin antibodies (TG ab). Why did the doctor start reducing your med when TSH came down within range?
You are going to need additional testing to see where your thyroid hormone levels are. Specifically you should always get tested for both Free T4 and Free T3 every time you go in for tests. In addition, hypothyroid patients are so frequently deficient in Vitamin D, B12 and ferritin, that those should be tested and supplemented as needed to optimize. D should be at least 50 ng/mL, B12 in the upper end of its range, and ferritin should be at least 100.
You can confirm all this in the following link. I highly recommend reading at least the first two pages, and more, if you want to get into the discussion and scientific evidence for all that is recommended. You may also find the paper useful in discussion with your doctor, in order to try and get the testing and treatment needed. If your doctor is unwilling to treat clinically, as described above, then you will need to find good thyroid doctor that will do so.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf