Getting off birth control

Cassy • 👶 07/16/19, ttc #2!
I just stopped taking birth control a couple days ago and I've heard two different things about stopping. One is that it takes a few months for the birth control to get completely out of the system so it's unlikely to get pregnant at first. Second is that you are super fertile right after stopping birth control. Just wondering if anyone could give me some insight to this. I've been on the pill for close to two years if that helps any. Thanks everyone!