If the drill bit snapped, it was due to mechanical force, probably bending. Since the drill bit is much harder than the brass nozzle, it's probable that force that broke the drill bit also damaged the nozzle. There's no point in trying to get the piece of drill bit out- you need a new nozzle.
Ultra MegaMax Dominator 3D printer: [
drmrehorst.blogspot.com]