I took Yaz for 3 months and it totally screwed up my body. My periods were light and extremely painful and lasted for 10-12 days. As soon as I went off of it I felt so much better. I went right back to a heavy period that lasted 5-6 days after exactly 30 days off the pill.
Birth control pills are effective in preventing pregnancy after only 7 days. It doesn't take months. You probably got confused in that doctors usually tell you that it takes your body about 3 months to become regulated while on the pill. Meaning that your periods will be strange for the first few months. My doctor told me that she has found it takes more like 6 months for your body to fully adjust.
But you are definitely protected against pregnancy after just a week. And you don't ovulate while on the pill. And if for some reason you do happen to ovulate then the super thick mucus the pill makes totally kills the egg.
You only have less than a 1 in 100 chance of getting pregnant on the pill so I wouldn't worry about it.