Is there a mental disorder where a person feels like everything is their fault?

This can be a symptom of several mental disorders, but itself is not a mental disorder.

This delusion is one type of of "paranoid" symptoms (i.e. that you are the cause of everything - in this case everything bad) and is common in depressive psychosis (clinical depression with psychotic features). But such delusions also occur in other mental disorders having psychotic features (e.g. paranoid schizophrenia).

I have Bipolar disorder and although I have never had depressive psychosis in any of my episodes, I have had a related paranoid delusion that it was my responsibility (and I somehow had special abilities needed) to fix everything bad when I was in a manic psychosis. I did not think I caused them, just that I had to fix all of them.