Antibiotics?

Laura
Hi ! 
I have a very very very bad cold. Today, I went to the doctor and he prescribed a Z pack along with Mucinex. Yesterday was my last placebo pill, and today I'll be starting a new Pack of BC. 
I know antibiotics make birth control less effective, but can those two things I got prescribed cause my BC to not be effective? Should I use a backup method? And if so, for how long? 
I'm just trying to play it safe, and this is my first time taking antibiotics + BC. 
Thank you!