headache vs vexation

headache and vexation both are nouns.

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

As nouns, headache and vexation are synonyms defined as:

headache and vexation: something or someone that causes anxiety; a source of unhappiness

Other synonyms of headache include concern, worry.

headache (noun)	vexation (noun)
something or someone that causes anxiety; a source of unhappiness	the act of troubling or annoying someone
pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs	something or someone that causes anxiety; a source of unhappiness
	anger produced by some annoying irritation
	the psychological state of being irritated or annoyed