Birth Control + Antibiotics

Sky
Hi! So I am starting Accutane for my acne. I'm 17 years old. I just started my second month of my Trinessa birth control pills.
Last month for the first two weeks of my birth control, I took Doxycycline which is an antibiotic for my skin. It was supposed to hold me over until I can get on my Accutane. I know that antibiotics cancel out birth control. 
I just started my second month, 2 days ago on Sunday Feb 19.
Is this month's birth control going to be affected by those antibiotics? I'm not sure how medications like this work. Did the second half of my last month's birth control completely get canceled out as well as the first half?
Sorry, I don't want to sound uneducated. This is my first time ever being on birth control and I just want to be safe. I didn't get a chance to ask my doctor these questions.