Just a few thoughts, but by your own admission you do care for your family, did care for your girlfriends, were upset by your grandmothers death and do feel towards fictional characters. Just because you don't feel as deeply, or show as much affection as others, doesn't mean you don't love them

and it seems that you not feeling deeply eats up at you, isn't that in some ways, remorse for not being a certain type of person? What matters just as much, if not more, is the action. You can feel love, empathy and remorse, but if that's not shown through your actions, then it doesn't actually help those around you. The steps you're currently taking to improve yourself sounds like an act of love,. It might not be grand, but nonetheless it's something you're doing for the benefit of others. If that's not the definition of an act of love, at the very least, it's an act of good, and I think that's what matters more.