Does NFP really work?

I am not Catholic yet, but will start taking the RCIA classes. So, I have been reading up on Catholicism. I read that using condoms is a mortal sin.

This really stresses me out because I do not want to commit a mortal sin, but I don't want to get pregnant either. After my last baby, the doctor suggested I not have any more children because I had extreme post-partum and wanted to kill myself.

So, it seems from what I've read that NFP is my only option. But, doesn't that have a high failure rate? I realize I'm not educated at all about NFP either. Advice please?