Think that I could be pregnant but still taking my birth control

So I take my pill at like a different time each night. But within a 2 hour time frame of 9pm. So I got drunk one night and I still managed to take my pill but I took it at like midnight. That night I had unprotected sex with my SO. The past couple of days I've been feeling sick but I keep telling myself that it's just allergies. So my question is- if I am pregnant, would my birth control hurt the fetus?