no you havent done anything wrong, if the relationship wasnt working out you have every right to not want to be in it anymore. you even have every right to go out with anyone you like after regardless of how long its been, youre your own person now, so you can do what you like.
But stop rubbing it in his face, hes obviously still hurting, hes definitely not over you yet, and youre being completely heartless. Yes you share friends, but youre the one whos come out better in all this, stay away from him for a bit, see your mutual friends less for a while, he needs them more than you at the moment. and when he starts to get better, you can start being normal again.