If you are on your parents insurance, then they would probably find out.

A suggestion might be to have a brief conversation with them how all these things going on you would like to talk to a Therapist. Once in with the Therapist you can be open and honest.

Having a 10 year old son come to me and indicated he wanted to talk, there was no questions asked. Of course my ex and I have some issues of our own.

Anyway it normally takes anywhere from a week to a month to see someone. Set the appointment, then have the convesation with your parents.