After watching Iron Man 1 yesterday, my appreciation for Tony's character arc has gone up quite a lot, yet again. And Iron Man 3 makes sense, when it comes to Tony.
In part 1, he had this big epiphany about his life and that it needed a new direction. He was taken from the edge of death, and given a new lease on life.
In part 2, he's a bit of an arrogant prick, but we realise that he is still dying, but now because of the invention that supposedly saved him! That does a lot to a man. Plus, all the good things he can do now as Iron Man will be lost on the world when he's gone. He's so protective about safe-guarding his armour from the military, because he has no idea what's going to happen with this tool for doing good after he dies and the military will get their hands on it. Thankfully, he's both able to safe his life again, and make sure the armor can stay away from the military.
Now, the Avengers.... Tony finds out, that after all, he is still mortal. The chestpiece keeps him alive from the shrapnel and the newer version isn't lethal anymore. But despite all the strength his armour gives him, he can still be killed and almost was. And not just that, that means he's not capable of simply stopping all threats just by showing up and doing his Iron Man thing.
Enter Iron Man 3.... Tony's on edge. So worried about not just protecting himself, but also the people he loves, he is on a continues quest to better his armour, making different versions for all kinds of calamities, trying to make sure he is always prepared. He loses himself in it, it drives him and seperates him from the ones he loves, to a point where he has panic attackes and is always questioning his abilities. Ultimatly, he learns that not only is he capable of achieving victory without the armours, his loved ones are quite capable of protecting themselves, and if need be, him.
And that's what the last line in the movie means. In part 1, it was 'I am Iron Man', with the emphasis on Iron Man. Now, the emphasis is on 'I', meaning Tony is himself.