There is no good way to handle it.
However, your question is very significant. Notice that your question is focused on two topics: self harm and your parents, specifically your parents’ reaction to your self harm.
I remember when I was feeling a little suicidal in my 20s a therapist asked, “And who would find your dead body?” My parents!
He suggested I might be a little angry at my parents, if in all my fantasies my parents were the ones to find my dead body.
“Oh, no! I wouldn’t want to hurt them. That’s why I resist killing myself, so as not to hurt my parents.”
“But in all your fantasies your parents are hurt by discovering your dead body.”
So I kept a dream diary for a while. I had a dream that a woman was having a garage sale and she was selling five squashed babies. “You don’t get into trouble with the state if you report it within 24 hours, she said.”
My mother loved garage sales. She had 5 boys, even though she wanted a daughter, not sons.