i wished you had said which county you are in, it is good that they even let you apply. how old were you when the incident happened. since it is a violent crime could be one of the reasons it was denied.
you can appeal to the chief justice in your county, and if that doesn't work you can go to the AG.
anyone can give you a gun as long as you are not a unallowed person (felonies or domestic charges). as long as it is in your possession you "own" it. guns are not registered in NC.
a FFL background check is not the same as what the sheriff dept. did. they actually used their personal bigotry to deny you.