Prozac and Birth Control Pills

I've just started taking Prozac 20mg for anxiety and depression, and about 2 days after I started taking it, I started spotting. I've been on birth control for almost 2 years now, and the only time I ever really spot is when I'm super stressed. Does Prozac affect birth control? I have had unprotected sex about 5 days before I started the new medicine so I am concerned. Also, I take the two meds at the same time every day.