In any case, it's good that you're talking to someone
This is a good decision! I'm not sure if she'll say anything, although most counselors are supposed to keep things confidential. I've talked to you before, and it seems like all of this could provoke her to say something to the parents. I want to you be sure that you can tell her about your family, too. Keep your points clear, and not just bugged out and with holes. Like this:
I don't want my parents to know, because I think they would hurt me for it (or something along the lines of that, depending on your situation)
I don't want my parents to know, because they're just like that.
I hope that helps