A starting dose of 25 mcg of T4 usually accomplishes nothing. The reason is that the med will cause the TSH to go down and that results in less production of natural thyroid hormone. Since serum thyroid levels are the sum of both natural thyroid and thyroid med, the level may not increase at all until the TSH is diminished to a low enough level that it no longer stimulates the thyroid gland, At that point, further increases in thyroid med will cause an increase in Free T4 and Free T3 levels.
At this point there is insufficient evidence that your hypothyroidism is the sole cause for your symptoms. You need to always test for both Free T4 and Free T3 every time you go for tests. Free T3 is the thyroid hormone that affects all the cells in your body and it correlates best with hypothyroid symptoms. In addition, hypo patients are frequently too low in the ranges for Vitamin D, B12 and ferritin, so you need to test those and then supplement as needed to optimize. D should about 50 min., B12 in the upper end of the range, and ferritin should be 70 min.
Two other tests I suggest are cortisol and Reverse T3 (with a Free T3 done from the same blood draw).
If you are able to get those done, then post results here and we will be happy to help interpret and advise further.
Be aware that a good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results.