1548, "a pinch," from obsolete verb twinge "to pinch, tweak," from O.E. twengan "to pinch," of uncertain origin. Meaning "sharp, sudden pain" is recorded from 1608. Fig. sense (with ref. to shame, remorse, etc.) is recorded from 1622.
I was very surprised to see that this was such an old word!
It has to be related to twang, as well, doesn't it?