on selfishness (?)

let's put this into perspective: a selfish person(or a self-centered person, or an egoist person - can someone enlighten me about the differences?) is someone who cares only about him or her self, someone who doesn't like to share things with others. i, for example, ofrten define myself as selfish, not because i don't like to share stuff, but because i tend to think about me first, and put myself first in most situations (also because i'm quite individualist). so my happiness always comes first - or should come, in theory. anyway, now let's imagine (just imagine, it won't hurt) that i obtain happiness by helping others, by helping them in any way i can. in other words, if i help, i'm happy. so does that means that, when i help someone out, i'm acting in a selfish way, because i'm not helping because i care about that person, but rather about my own happiness?