be sick vs vomit

be sick is not a noun while vomit is a noun.

Word	Noun	Adjective	Verb	Adverb
be sick	No	No	Yes	No
vomit	Yes	No	Yes	No

As verbs, be sick and vomit are synonyms defined as:

be sick (noun)	vomit (noun)
	the reflex act of ejecting the contents of the stomach through the mouth
	a medicine that induces nausea and vomiting
	the matter ejected in vomiting

be sick (verb)	vomit (verb)
eject the contents of the stomach through the mouth	eject the contents of the stomach through the mouth