get under one's skin vs bother

get under one's skin is not a noun while bother is a noun.

Word	Noun	Adjective	Verb	Adverb
get under one's skin	No	No	Yes	No
bother	Yes	No	Yes	No

As verbs, bother is a hypernym of get under one's skin; that is, bother is a word with a broader meaning than get under one's skin:

Other hypernyms of get under one's skin include annoy, chafe, devil, get at, get to, gravel, irritate, nark, nettle, rag, rile, vex.

get under one's skin (noun)	bother (noun)
	something or someone that causes trouble; a source of unhappiness
	an angry disturbance

get under one's skin (verb)	bother (verb)
irritate	cause annoyance in; disturb, especially by minor irritations
	make confused or perplexed or puzzled
	make nervous or agitated
	intrude or enter uninvited
	take the trouble to do something; concern oneself
	to cause inconvenience or discomfort to