No, being nervous about all of this is natural. I mean grad school is a big step for all of us, and we're likely going up against the best and brightest. Many of us have little idea of what we're doing and not living up to expectations is a common fear. And that emotion can muddle the excitement and that is OKAY. It shows you truly value your position (a very envious one) and like everyone else, you want to do well.
As for getting your offer rescinded: did passing those last classes involve blackmail or some kind of felony? If not, what you described seemed fine. I've heard of someone else on this board describe dropping a class late into the semester after having been accepted, and was told that would not affect that person's acceptance. But don't take my word for it, contact your respective DGS'es and ask. They'll probably be fine with it.