What can I do about my baby situation?

In my previous relationship my ex was on the pill, (we had discussed that neither of us wanted children yet), we were having what I though was safe sex (as she was on the pill) but she took antibiotics (unbeknown to me) and after the relationship was over she told me she was pregnant, honestly I don’t want anything to do with my ex or the child she says is mine, I feel like I’ve been forced and trapped into this hell that I cannot control, I feel like the system is flawed for situations like this as I have basically been forced into having a child that I am not ready for and do not what, I will not be put on the birth certificate. What can I do or is there anything I can contest?