@jreidy - This is probably one of the trickiest things in Korean. I'm sure I still mix up 은/는 and 이/가 sometimes.
To be honest, my best answer to your question "Why not say 내일 제가 일해요?" is that it just sounds weird. I don't know that there is a rock solid explanation for this, or one that makes it clear in all circumstances which one you're supposed to pick. Absorb what you can through explanations of these different particles, then just try to gather enough examples of each so you get a better feel for the nuance.