I'm sorry you don't have much support by way of family or doctor. Would talking to someone at school be an option? They may have to inform your parents, but it may also get you some more help. My guidance counselor was my lifeline in school. It helped to have the support of someone while I had nothing at home.
As for the cut, it should heal, as everyone else has said. I'm not sure what you mean by "normally" but it should heal with some scarring. Careful with the cutting. While you won't likely hit any major blood vessels, you could do muscle damage with deeper cuts. Just something to think about... Good luck Hon. I hope you can find some meaningful real life support (not just online).