There are other factors too.

If you are low in zinc and selenium, you cannot convert thyroid hormone in the tissues properly.

If you take other drugs that deplete things, that could be additive. (like Depakote, prednisone etc.).

I just posted this link on PN, so it might help you too:
http://www.webmd.com/skin-problems-a...uced-hair-loss
Please notice that Coumadin is on this list.

If you take birth control pills, some women get hair loss from progesterone.

Not enough protein in the diet?

MSM which is sold for arthritis relief, really improves hair and nails. If you don't have a good source of sulfur in the diet like eggs-- this supplement may help.
If you have elevated androgen levels in the blood, it might trigger hair loss too.

Heavy periods can lead to chronic low iron.
When you start to respond to the thyroid... it might fix the iron problems.
And I'd look into the gluten issue seriously too. If you do not respond to T4 Synthroid...you may need T3 added. You can discuss this with the doctor.
T4 has to be converted in the body to active T3...if you don't convert, you will not respond well to Synthroid. This is where zinc and selenium come in.

And make sure you take that thyroid on an empty stomach. Food interferes with absorption.
If you use a generic, I'd recommend Mylan over others. I don't like the Sandoz product.