Hi Pastel,
I'm sorry...Your father hasn't reacted adequatly. He should have tried to understand you and offer you support.
. Is this the first time your father heard about your SI?

How did he find out?
What to do now? Hmmm... Could you talk with your mother instead?
You want to see a psychologist, but..? You could tell your father that, as he put it, you don't want to be "messed up" in your head anymore, but to solve that, you have to see a psychologist...
I understand that you don't want to stop self harming. It's a "great" coping mechanism. I hope that, as soon as one starts to feel better, the self harming won't be needed anymore and stop anyway.
Take care