If I’m named as the executor or personal representative in the will can I start administering the estate in North Carolina?

No.  First, You must file the will with the probate court, establish the will’s validity, and be formally appointed executor or personal representative.  Before rushing off to the courthouse, you should be sure that you have the correct will.  Sometimes, a family member will find a will, assume it’s the right one, and head on down to the courthouse only to discover later that there is a more recent will or trust that replaced the revoked prior will.