Having thoughts of suicide and harming yourself is not a good thing, and yes, can be a sign of depression. Talking to someone is a good idea, could you go to a school counselor perhaps? You can talk to a school counselor without your parents needing to know (as far as I know) and it helps getting it out and talking to someone. Or, you could visit your doctor and talk with them about it. Telling your parents can be a good idea, it's good to have their support. But, without knowing your situation just do what you feels best for youself.
If your school doesn't have counselors, then talk to a trusted adult about things, about how you're feeling. If you're ever in a situation where you're having suicidal thoughts and have no one to talk to, you can always call a hotline:
National Suicide Hotline 1-800-SUICIDE
Youth Crisis Hotline 1-800-448-4663