Hi, Welcome to HCM.
I understand your concern. When you said that you reduced the dose of
thyroxine from 150mg to 125mg based on the available
blood test, I assume that you are indicating T4 levels and not
TSH levels. Because if your TSH levels are high then it means that your thyroid gland is under functioning (
hypothyroidism). In this case you will need to increase your thyroxine and not reduce it. Regardless, your symptoms should also agree with your lab results. Based on the information you have given (weight gain, feeling sluggish and tired) these go in the direction of hypothyroidism meaning that you will need to increase your thyroxine. I will advise you to consult your primary physician for the same since the doctor will need to titrate the dose of thyroxine based on the clinical condition (lab results as well as symptoms).
In contrast, when your T4 is high it is assumed that it gets converted to T3 in peripheral tissues if blood levels are not available. In this regard, you are right and the only way to find out about the T3 levels is to get it checked. Majority of the times when we prescribe thyroid function test it includes T3 in addition to TSH and T4 levels.
You have also mentioned that you are on other medications particularly statins. Looks like your lipid levels are high. In this regard, I will advise diet control and exercise that will help improving your general well-being. However, I would wait until you are done with your cardiovascular examination and ask your cardiologist about the same.
Hope this helps.