mess up vs mess

mess up is not a noun while mess is a noun.

Word	Noun	Adjective	Verb	Adverb
mess up	No	No	Yes	No
mess	Yes	No	Yes	No

As verbs, mess up and mess are synonyms defined as:

mess up (noun)	mess (noun)
	a (large) military dining room where service personnel eat or relax
	a meal eaten in a mess hall by service personnel
	soft semiliquid food
	(often followed by `of') a large number or amount or extent
	a state of confusion and disorderliness
	informal terms for a difficult situation

mess up (verb)	mess (verb)
make a mess of or create disorder in	make a mess of or create disorder in
disturb the smoothness of	eat in a mess hall
make a mess of, destroy or ruin