If you're self-harming, I believe you need more care, but you can address it in different ways than therapy if that's what you need to do instead or to start with. That split you're referring to is concerning. Most family are not at all equipped to deal constructively with self-harm, so there's nothing wrong with you for not being helped by their responses. I would suggest consulting with your GP and considering the different types of specialists and finding someone, some partner, some system to help you.