Birth control patch and migraine medication

Hey ladies! I have been experiencing some bad migraines. I have which went to the hospital for 2 times and I have a appointment soon for. BUT the medication I got prescribed (butalbital-acetaminophen-caffeine) and it lowers the effect of my birth control. I got told I’m very limited to medications due to my birth control. I am wondering if anyone has had this issue and if so what did you do? Thank you! 💕