You are not obligated to tell anyone if you don't want to. As a parent I wouldn't be disappointed in my daughter, I would be more disappointed in myself if she felt she couldn't tell me. You can start with your parents and take it from there. You might be surprised by how supportive they just might be.
It's not an easy thing to admit to anyone. I'm glad I told my mom as she is one too and understands how this is for me. And I understand her better too.