health problem vs unhealthiness

health problem and unhealthiness both are nouns.

Word	Noun	Adjective	Verb	Adverb
health problem	Yes	No	No	No
unhealthiness	Yes	No	No	No

As nouns, health problem and unhealthiness are synonyms defined as:

health problem and unhealthiness: a state in which you are unable to function normally and without pain

Other synonyms of health problem include ill health.

health problem (noun)	unhealthiness (noun)
a state in which you are unable to function normally and without pain	a state in which you are unable to function normally and without pain