fed up vs sick of

fed up and sick of both are adjectives.

Word	Noun	Adjective	Verb	Adverb
fed up	No	Yes	No	No
sick of	No	Yes	No	No

As adjectives, fed up and sick of are synonyms defined as:

Other synonyms of fed up include disgusted, sick, tired of.

fed up (adjective)	sick of (adjective)
having a strong distaste from surfeit	having a strong distaste from surfeit