Yes, we have had members report hair regrowth. I expect it would be at least several months after getting thyroid hormone levels and the other variables mentioned to optimal levels.
A starting dose of thyroid med, like your 50 mcg of thyroxine, does not add to your serum thyroid levels. Instead, the med causes TSH to drop, resulting in less stimulation of the thyroid gland, and less output of natural thyroid hormone. Serum thyroid levels are the sum of both natural thyroid hormone and thyroid med. So, only when your med dose is enough to essentially suppress TSH will further increases in the med cause your serum thyroid levels to start to rise. Note the following conclusion from a recent, excellent scientific study: "Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and Free T3 elevated further into the upper half of its reference range." Sometimes the patient will find that a source of T3 is also required to raise Free T3 to levels needed to relieve hypo symptoms. If not tested since starting on the 50 mcg of thyroxine, you need to test for Free T4, Free T3, revere T3 (at least once to assure okay), cortisol, and TSH just to determine when it becomes suppressed below range. Note that med dosage should never be determined by TSH, but as needed to relieve hypo symptoms.
In addition, hypothyroid patients are frequently deficient in Vitamin D, B12 and ferritin so you should also get those tested and supplement as needed to optimize. D should be at least 50 ng/mL, B12 in the upper end of the range, and ferritin should be at least 100. Hair loss like you mention is likely due to inadequate thyroid hormone levels and also low ferritin.
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.