Birth control

So I’m 18, and I would like to get on bc because my boyfriend and I have had a few slip ups while having sex. (As in we’ve literally taken 3 plan b’s. Lord help us). But the only thing is I was raised with extremely strict parents who believe that sex is saved for marriage. Which is cool for them but for me that just didn’t happen. How would I get on bc in Texas without it showing up on my insurance? It can’t go through my insurance right? But how much would it be and what would be my best option.

And we used protection but it always ends up breaking or just not being comfortable so we take it off and he pulls out. I know it’s not the safest but we still do it and there’s really no changing it.