get under one's skin vs get to

get under one's skin and get to both are verbs.

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

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

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

get under one's skin (verb)	get to (verb)
irritate	arrive at the point of
	cause annoyance in; disturb, especially by minor irritations
	reach a goal