Yes, in fact antibiotics can interfere with the Pill which is why Drs may recommend to take extra precaution (use a condom as well) when you are prescribed an antibiotic and are on the pill. Taking an antibiotic will not impact conception or implantation of an embryo.
Why are you taking an antibiotic for back pain? do you mean a pain reliever??
Wait is out and test if you are late, that is the only thing you can do at this point.