Yes it sounds like the nerve has died, you need to keep an eye out for a gum boil (pimple) which will indicate an infection as the dead nerve will decay therefore often causing an infection, the gum boil will drain the pus out, pain will also indicate an infection, be prepared for the possibility that it 1) may need removing, 2) need a pulpotomy (removing the dead nerve chemically) 3) that it remain like that until it falls out naturally.