my parents are making me feel bad about going to the mental hospital

I’ve (16) recently been having thoughts about harming myself and told my teacher yesterday, then the police came to my house to do a welfare check and they told us to go to the hospital. My parents were VERY mad at me and were like ‘you know that’s wrong’ ‘don’t do that again’ ‘why did you do that?’

but is it my fault for feeling this way? why should I feel guilty about thoughts I can’t control or how I feel towards myself and my life?