If it only bled for a couple of minutes and stopped, it's fine. You probably didn't do any permanent damage, either.
It is a scary place to cut yourself, but I can promise you that doctors, should you ever need one for your genitals (and you will at some point) have seen it all. You aren't nearly the first one to cut yourself shaving. Men and women have cut themselves trimming with scissors. (This hurts - I know firsthand.)
So you're fine, and no need for worry or embarrassment. :)