Birth Control Pills - Hair Loss

I recently started my first pack of Yaz. I noticed that more and more hair is going down the drain. And even if I just comb my hair using my hand! I'm losing so much hair. I don't want to go bald. I've been taking supplements and vitamins for my hair ever since because it's really thin. I've doubled the dosage now and nothing's changed.  Has anyone experienced this? And any recommendations?