I agree with FinnMaid - it's really best to have a FreeT3 level done to confirm the need for T3. And, additional testing seems most appropriate.
Low FT3 levels can cause hypo symptoms. (so can low FT4 levels...)
Cytomel is usually best taken in divided doses since it has a short half-life. So, rather than take 2 tabs in the morning, you might want to take 1 in the morning and the other 6 hours later (this takes into account the half-life). Consistency with dose timing feels better, by the way.
Symptoms can improve within a few weeks of starting but, full symptom elimination doesn't happen until after the FreeT4/T3 levels are optimized....this can take some time.
Please know that hair has thyroid hormone receptors and is therefore very sensitive to too-low thyroid hormone levels, too-high thyroid hormone levels and/or moving thyroid hormone levels. You have the first and the last going on right now so, hair loss is likely to continue.
In addition, the hair growth cycle is 3 months so, it's not until after we are stable at our optimal levels that re-growth will become noticeable.
Best of luck to you moving forward!