BC and Antibiotics

Hey Ladies!
I need some advice...
1. My doctor recently prescribed me an antibiotic for a sinus/ear infection.
And
2. I lost one of my Birth Control pills (down the sink), so am now "skipping" a pill. 
My question is, how long should my SO and I use a back-up method of birth control? I know that the antibiotic "cancels out" the BC, but since I lost a pill, I'm now doubly anxious about a back-up. 
Thank you for your advice! I love that we are ladies helping ladies.