I feel self-reproach for that act.
自責 means 'self-blame' or 'self-accusation' and is more common in modern Japanese for general self-reproach, whereas 呵責 is largely confined to the fixed expression 良心の呵責.
Standard kanji spelling.
Rarely used kanji form.
The kanji 呵 means 'to scold' or 'to blame', and 責 means 'responsibility' or 'blame'. The compound originally referred to severe blame or torture, but in modern Japanese it is almost exclusively used in the phrase 良心の呵責.