Focusing on the feelings of people is Ethics, Fe approaches it differently than Fi, Fi deals with the personal attitudes towards something/someone, and Fe with a more "general" stance on them that's not directly linked to personal preferences, hence slightly less personal compared to Fi. Example of the latter from an EIE explaining:
http://www.the16types.info/vbulletin...=1#post1167012
In your example, the part about focusing on whether you have any feelings was really Fi to me. Could be your Fi demonstrative, with some Fe intent in the expression, of course, it's slightly ambiguous for the rest of what you said.