Please post your thyroid related test results and reference ranges shown on the lab report. Also, if tested for Vitamin D and ferritin, please post those as well. Please also tell us about all symptoms tht you have.
There is a lot to discuss. First is that hypothyroidism is not just "inadequate thyroid hormone'. Instead it is correctly defined as insufficient T3 effect in tissue throughout the body due to inadequate supply of, or response to, thyroid hormone. So it is not just thyroid hormone, but the response to it that is important. And there are a number of variables that affect the response. So it is the TISSUE T3 EFFECT that determines your thyroid status. There are no blood tests that measure TISSUE T3 EFFECT. There are no blood tests that even correlate with TISSUE T3 EFFECT well enough to use as sole diagnostics for your thyroid status, or to determine your medication dosage.
Your thyroid gland produces mostly T4 and some T3 thyroid hormones. Most of that is bound to protein and rendered inactive. Only a small portion of each is free of protein and thus biologically active. Those are Free T4 and Free T3, both of which should be tested every time you go in for tests. TSH is a pituitary hormone that doctors erroneously think gives them all the info they need to diagnose and treat hypothyroidism. That is very wrong. TSH does not even correlate well with either thyroid hormone Free T4 or Free T3, and has only a negligible correlation with hypothyroid symptoms, which are the reason you went to the doctor in the first place.
Doctors say that symptoms are non-specific and that is true for any individual symptoms; however when you have multiple symptoms that are typical of hypothyroidism, that is the best diagnostic for the possibility of hypothyroidism. That then should be followed up with tests for Free T4 and Free T3 to support the finding from an evaluation for symptoms.
So, before going further please tell us what symptoms you had when first diagnosed as hypothyroid, and what symptoms did you have when taking the 125 mcg of T4.
A couple of additional things I want to point out is that in the untreated state, your body is used to a continuous low flow of thyroid hormone from the gland. When taking a significant daily replacement dosage of T4 med in a single dose it spikes the FT4 level, and to a lesser degree also spikes the FT3 level, which causes suppression of TSH for most of the day. So a suppressed TSH in the treated state does not mean the same as in the untreated state. When taking the thyroid med, a suppressed TSH indicates over treatment and hyperthyroidism only when there are also hyper symptoms due to excessive levels of Free T4 andFree T3. However, most doctors erroneously interpret a suppressed TSH as over treatment and want to reduce the med dosage.
So if your doctor is medicating you only enough to get your TSH back within range, that typically results in under treatment. Also when taking T4 med there is usually inadequate conversion of T4 to T3, so the FT3 level lags the changes in FT4 and remains too low. You have to have adequate levels of Free T3 to achieve adequate TISSUE T3 EFFECT. There is a recent, excellent study that quantified for the first time the effect of FT3 on the incidence of hypo symptoms. The authors concluded that " Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and FT3 elevated further into the upper half of its reference range".
You haven't even been tested for Free T4 and Free T3, so that should be the first priority to get done. You need to know if those levels are too low and causing hypo symptoms. Your response to the higher dose and the reaction to lowering the dose could be a reaction to other variables such as ferritin or cortisol, instead of being over medicated. You can only know that by getting tested for FT4, FT3, cortisol, and ferritin. Those are some of the most important variables regarding the response to thyroid hormone. In addition hypo patients are frequently deficient in Vitamins D and B12, so those need to be tested as well.
Even though you feel some short term relief from lowering the dose, you cannot know if that is the right thing overall without getting the additional testing done to better understand the cause(s) for your symptoms.
If you want to confirm what I have said, click on my name and then scroll down to my Journal and read at least the one page Overview of a paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective. You should also make a copy of the Overview and give it to your doctor if needed to persuade him to do the additional testing needed.
Keep in mind that a good thyroid doctor will do the recommended testing and treat clinically by adjusting FT4 and FT3 as needed to relieve hypo symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results. Other variables mentioned also need to be tested and optimized to provide maximum benefit.