North Carolina does not recognize common law marriages regardless of duration. However, depending on the circumstances, this person probably needs legal counsel to begin probate and work through this situation. OP, who paid your father's final expenses? Did you attend the funeral, help make the final arrangements?
What attempts have you made to talk to companion? Did father own property that you are aware of? In other words, is there an estate to deal with? Were you just expecting the companion to pay all the bills, settle the estate for you and send you a large share of money? When you are waiting for your share of the inheritance and asking how long does it take, it sounds as though you expect someone besides you to take care of this.