COMPELLED: You’ve no choice.
IMPELLED: To do something even if you may not like doing it; it’s the right thing to do.
(Example: when I was a kid, I sometimes took small change from one of the drawers in my parents’ dresser, went to the store on the corner, and bought goodies. Mostly candy. If I had had a bigger conscience at that time, I would have felt impelled to confess. But I didn’t. My conscience was still being formed. Instead, I was compelled to tell the truth because I was caught in the act. Punishment followed.)