My hair is falling out on the contraceptive pill. Stop or brace it?

I was on the mini pill for a good 15 years before I decided to take a break for a couple years. About 3 months ago I went back in them. Cerazette. My hair is now falling out left and right. It's really scary! Is it better for me to stop the pill asap or is this hair loss pattern only suppose to last a few months and I should just bare with it? I'm 34 and take thyroxine for under active thyroid. My latest blood check shows normal levels. Please help!!