fellow feeling vs sympathy

fellow feeling and sympathy both are nouns.

Word	Noun	Adjective	Verb	Adverb
fellow feeling	Yes	No	No	No
sympathy	Yes	No	No	No

As nouns, fellow feeling and sympathy are synonyms defined as:

fellow feeling and sympathy: sharing the feelings of others (especially feelings of sorrow or anguish)

fellow feeling (noun)	sympathy (noun)
sharing the feelings of others (especially feelings of sorrow or anguish)	an inclination to support or be loyal to or to agree with an opinion
	sharing the feelings of others (especially feelings of sorrow or anguish)
	a relation of affinity or harmony between people; whatever affects one correspondingly affects the other