sick headache vs megrim

sick headache and megrim both are nouns.

Word	Noun	Adjective	Verb	Adverb
sick headache	Yes	No	No	No
megrim	Yes	No	No	No

As nouns, sick headache and megrim are synonyms defined as:

sick headache and megrim: a severe recurring vascular headache; occurs more frequently in women than men

Other synonyms of sick headache include hemicrania, migraine.

sick headache (noun)	megrim (noun)
a severe recurring vascular headache; occurs more frequently in women than men	a severe recurring vascular headache; occurs more frequently in women than men
a headache accompanied by nausea