labor pain vs hurting

labor pain and hurting both are nouns.

Word	Noun	Adjective	Verb	Adverb
labor pain	Yes	No	No	No
hurting	Yes	No	No	No

As nouns, hurting is a hypernym of labor pain; that is, hurting is a word with a broader meaning than labor pain:

labor pain: pain and discomfort associated with contractions of the uterus during labor
hurting: a symptom of some physical hurt or disorder

Other hypernyms of labor pain include pain.

labor pain (noun)	hurting (noun)
pain and discomfort associated with contractions of the uterus during labor	a symptom of some physical hurt or disorder