I was in my 30's when I was diagnosed and I didn't tell my parent's for nearly 2 years. It is tough.
But when I did tell them it was like this weight was lifted off my shoulders. This horrible secret I didn't have to hold in my heart anymore. And they loved me. They were very supportive. I wish now I would have told them what was going on in my head when I was a teenager. May have led me to being diagnosed and getting help a lot sooner.
Your parent's may not know what to do. They may even freak out or do stupid stuff, but I am willing to bet that they love you very much and if they knew what was going on - they would help you. You know your parent's best of course. I know that not all parent's are 'safe'. but if they have never hit you, only yell if you do something clearly wrong, and generally provide a good home environment, may be worth the risk.
Perhaps you could speak to a guidance counselor and they could see who to refer you to. Its best just to let them know what is going on as you have posted and they will know what to do from there. Talk therapists are generally supportive and take a helpful approach and psychiatrists know how to follow up with these concerns. If you have done anything thats self harmful its better to approach them now so they could help treat that and follow up.