Hi Gladys,
I'm on Copaxone too and notice my hair has been thinning in the past year or so. I'm on it almost 9 years though. I did get bloodwork done to check my hormones and thyroid and all was normal. I don't really know if it's the Copaxone or not in my case since I've been on it so long. My Ferretin ( Iron ) level was low last I got it checked and I'm on a daily Iron supplement. Just wanted to tell you, you're not alone and although I don't really have any answers, ( I wish I did) I can relate.