First of all, I'm going to assume you have a primary care provider, who can give you a referral to a psychiatrist. Telling your parents is not something you actually HAVE to do, but it would be a good idea to do so in order that they can give you some support. You never know, they might already have a notion that you need help---sometimes the people closest to us know the truth long before we figure it out.

I recommend seeing a psychiatrist first, as opposed to a psychologist or therapist, because they can not only diagnose you (or not), they can also prescribe medications if you need them. A therapist should be involved though, because you will need someone to talk to and many people only see a psychiatrist every few months for medication management. Your primary care provider should be able to recommend one as well.

I wish I knew more about your relationship with your parents so I could advise you better...you seem to be fearful that they will react badly if you disclose your feelings. Wishing you the best.