All the people who prescribe but have never taken Forteo will tell you that hair loss is not a side effect. Hair loss is a common complaint from people who have taken Forteo. Hair loss wasn't signaled in clinical trials. It possibly because nutritional values were also controlled.
Forteo is very good at depleting vitamin D by putting it to good use; low vitamin D can cause hair loss.
Some have reported that the hair recovers after two years of Forteo. Others have reported that the hair dosen't recover.
I haven't experienced hair loss. I have tripled D3 intake to keep a constant serum level.
Hyperparathryoidism does cause hair loss, I think it's Forteo causing you hair loss.