hemicrania vs sick headache

hemicrania and sick headache both are nouns.

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

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

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

Other synonyms of hemicrania include megrim, migraine.

hemicrania (noun)	sick headache (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