You don't mention your age, and women can have hair thinning, loss. But since you have had your hormone levels checked, we can assume you're not in menopause.

Anyway, I have only been on Copaxone about a year, but I do notice my hair has begun to thin, and more comes off on my brush now than before. And the oddest thing: it doesn't grow anymore. I haven't had a haircut in 8 years! Only trim my bangs. I had put it all down to menopause. But now I'm not so sure. Maybe its not the meds, but MS?