Can I sue the other woman for alienation of affection?

If you are able to get proof of this affair, then in NC you may be able to sue your spouse's lover if certain legal requirements have been met. "Alienation of Affection" is a legal action based on willful and malicious interference with marriage relations by a third party (these actions are often brought along with "Criminal Conversations" actions. 

For a plaintiff spouse to recover for alienation of affection, the following elements must exist: (1) the parties to the marriage were happily married and genuine love and affection existed between them; (2) such love and affection was alienated and destroyed; (3) and the wrongful and malicious acts of the defendant brought about the loss and alienation of such love and affection. The exclusive right of sexual relations is not the right protected in such case as this; the actual affection between spouses is the right protected.

Criminal conversation is a claim for adultery. Unlike alienation of affection, this action does protect the fundamental right of exclusive sexual relations between spouses. To prove a cause of action of criminal conversation, the plaintiff must be, or have been at the time, lawfully married and their spouse had sexual intercourse with the defendant without the consent of the plaintiff during the marriage.  It does not matter if the plaintiff and their spouse were separated at the time.