sympathy vs fellow feeling

sympathy and fellow feeling both are nouns.

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

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

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

sympathy (noun)	fellow feeling (noun)
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)
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