sick headache vs headache

sick headache and headache both are nouns.

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

As nouns, headache is a hypernym of sick headache; that is, headache is a word with a broader meaning than sick headache:

sick headache: a severe recurring vascular headache; occurs more frequently in women than men
headache: pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs

Other hypernyms of sick headache include cephalalgia, head ache.

As nouns, headache is a hypernym of sick headache; that is, headache is a word with a broader meaning than sick headache:

sick headache: a headache accompanied by nausea
headache: pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs

Other hypernyms of sick headache include cephalalgia, head ache.

sick headache (noun)	headache (noun)
a severe recurring vascular headache; occurs more frequently in women than men	something or someone that causes anxiety; a source of unhappiness
a headache accompanied by nausea	pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs