(Oh, now isn't that interesting. Megrim and migraine have the same root. As well they might: megrims are the migraine of the soul. According to Meriam-Webster:
Megrim and "migraine" share a meaning and an etymology. Latin and Greek speakers afflicted with a pain in one side of the head called their ailment "hemicrania" or "hēmikrania," from the Greek terms hēmi-, meaning "half," and kranion, meaning "cranium." French-speaking sufferers used "migraine," a modification of "hemicrania," for the same condition. English speakers borrowed "migraine" from French - twice. First, they modified the French term to form "migreime," which in turn gave rise to "megrim" in the 15th century. Later, in the 18th century, they returned to French and borrowed "migraine" again, this time retaining its French spelling. Nowadays, "megrim" and "migraine" can still be used interchangeably, but "megrim" can have other meanings)