Old English cwealm (West Saxon) "death, murder, slaughter; disaster; plague; torment," utcualm (Anglian) "utter destruction," probably related to cwellan "to kill, murder, execute," cwelan "to die" (see quell). Sense softened to "feeling of faintness" 1520s; figurative meaning "uneasiness, doubt" is from 1550s; that of "scruple of conscience" is 1640s.
Evidence of a direct path from the Old English to the modern senses is wanting, but it is plausible, via the notion of "fit of sickness." The other suggested etymology, less satisfying, is to take the "fit of uneasiness" sense from Dutch kwalm "steam, vapor, mist" (cognate with German Qualm "smoke, vapor, stupor"), which also might be ultimately from the same Germanic root as quell.