First thing we need to discuss is that TSH is a pituitary hormone that is affected by so many things that, except at extreme values, it is inadequate as a diagnostic for thyroid status, since TSH has only a weak correlation with the thyroid hormones, and a negligible correlation with symptoms, which are the patients' concerns. Far better indicators of thyroid status are symptoms, along with the biologically active thyroid hormones Free T4 and Free T3 (not the same as Total T4 and Total T3).
So, it may be the standard of care for your doctor to diagnose and treat you based on TSH, but that is incorrect. A tentative diagnosis of hypothyroidism should be based first on symptoms that occur more frequently with hypothyroidism, followed by confirmation with tests for at least Free T4 and Free T3, If the patient has several symptoms that are frequently related to hypothyroidism, like fatigue, dry skin, weight gain, slow movement, and constipation, and Free T4 and Free T3 are in the lower part of their range, then that is possibly hypothyroidism and the patient should be given a therapeutic trial of thyroid medication adequate to raise his FT4 and FT3 into the upper half of their ranges and evaluate the effect on symptoms. If symptoms ease, then that is confirmation of hypothyroidism.
Another important consideration is that a starting dose of thyroid med (like your 50 mcg of Eltroxin) does not raise your FT4 and FT3 levels. The med dose causes TSH to go down, and thus reduce the output of natural thyroid hormone. Since serum levels are the sum of both natural thyroid hormone and thyroid med, only when TSH is suppressed enough to no longer stimulate natural thyroid hormone production will serum thyroid levels reflect further increases in thyroid medication. So TSH levels cannot be used to determine thyroid med dosage.
Getting back to your original diagnosis and treatment, were you tested for anything besides TSH? If not, then in addition to always being tested for Free T4 and Free T3, you need to test for the possibility of having autoimmune antibodies from Hashimoto's Thyroidis. Two tests are required: Thyroid Peroxidase antibodies (TPO ab) and Thyroglobulin antibodies (TG ab). There is more to discuss, but first please tell me about any symptoms you were having when originally diagnosed, and post any other test results you have that are related to thyroid..