I too had trouble with parents refusing to accept my struggles. I even told my mom I was suicidal and she told me to stop self-diagnosing. I hated that everyone doubted what I knew without any doubt was true. We can't diagnose you here, but the only thing that really matters is that you are worried. Even if you do not have a diagnosable illness, if it's bothering you, it's important.
In general, I would say feeling suicidal for any longish length of time is not normal and needs treatment, as does self-injury. On the other side, any delusions or hallucinations are not normal. Hang in there.