Self-harm in itself is not a diagnosis. For the vast majority of young people who self-harm, self-harm is an expression of difficult or unbearable emotions. Young people who self-harm may be referred to mental health teams for additional support; a psychologist or community nurse may be able to offer Cognitive Behavioural Therapy (CBT) which can help change patterns of thought and behaving.
Some young people who self-harm may be diagnosed with additional mental health problems, which can be confusing and upsetting. However, self-harming doesn't mean you have a mental illness – it is just one of the many things professionals will be looking for, in case there needs to be an additional diagnosis. In those circumstances make sure you ask questions, find out what it a diagnosis means for you and speak out if you don't agree.
Being part of the mental health system is nothing to be ashamed of, and a diagnosis is just a label - it doesn't take away who you are or what you can achieve in the future. Society still carries a lot of stigma about mental health, which is sad because it may stop people looking for help. If you want to be supported by professionals in overcoming your problems with self-harm, then go for it; if it's what you want to do it doesn't matter what anyone else thinks.