Barb49, Thyroid stimulating hormone (TSH) is a pituitary hormone which responds to thyroid hormone levels. Thyroid hormones are T4 and T3. When T4 and T3 are low, TSH rises. When T4 and T3 levels are good, TSH will be low.
Levothyroxine (T4) is the usual therapy to replace low thyroid hormone. Liothyronine (T3) is another therapy sometimes used in combination with Levothyroxine or on its own. Liothyronine often needs to be recommended by an NHS endocrinologist before it can be prescribed. Natural Dessicated Thyroid (NDT) is a combination of T4+T3 very rarely prescribed by the NHS as it isn't licensed for UK use.
Blood tests to determine whether thyroid replacement dose is adequate are usually TSH, free T4 (FT4), and sometimes free T3 (FT3). Post your results with the the ranges (figures in brackets after results) in a new question and members will advise whether you ar optimally medicated. When your thyroid levels and dose are optimal your hair should regrow.
Iron is usually measured via a Ferritin blood test. Ferritin is stored iron. Low ferritin can indicate iron anaemia and a full iron panel may requested if ferritin is below range. Ferritin <70 is low and can also be a reason for hairloss.
I am not a medical professional and this information is not intended to be a substitute for medical guidance from your own doctor. Please check with your personal physician before applying any of these suggestions.