Is there a single word that means "self flagellation" or "self punishment"?
Solution 1:
Asceticism is a form of self-denial, or voluntary suffering, especially as a way of life. It isn't always associated with guilt though.
Solution 2:
I can only think of penance, contrition and such words.
Solution 3:
Masochism? Or masochistic tendencies?
Solution 4:
Clinically, self-harm is grouped into different categories, but there doesn't seem to be one catch-all single-word term for it--just a collection of acronyms as outlined here from Wikipedia:
Self-harm (SH), also referred to as self-injury (SI), self-inflicted violence (SIV), Non-Suicidal Self Injury (NSSI) or self-injurious behaviour (SIB), refers to a spectrum of behaviours where demonstrable injury is self-inflicted. An example of self-harm/self-injury is cutting and is the second most common form of self-harm in the UK. The term self-mutilation is also sometimes used, although this phrase evokes connotations that some find worrisome, inaccurate, or offensive.
I've heard people who cut themselves referred to, nonclinically, as cutters. Of course, the more specific you get in terms of what harm is being done, the more choices there are for clinical terms describing that particular compulsion, e.g., bulimia, anorexia, trichotillomania, algolagnia, etc. Then there's the whole realm of body modification, and a host of other specific terms like scarification.
Solution 5:
Maybe it is too extreme but suicide is also a kind of self-punishment.