As you mentioned, North Carolina has a 'one time only' transfer rule for controlled substances in classes C III-V. This means that a controlled substance contained within those classes may only be transferred as a one time fill, regardless of how many refills are left on the original prescription.
However, per North Carolina law, if the pharmacies can communicate electronically in real time, with an online database, the entire prescription can be transferred. This would only be the case most likely if you are transferring pharmacies within the same chain (e.g. Walgreens to Walgreens).
I would get clarification from your original pharmacy in regard to what is going on.
Did they transfer the entire prescription to another pharmacy? Did they transfer one fill and cancel the rest? Is there another reason they are not allowing refills on the original? Is it expired? Get specifics from the pharmacy because if you don't have a valid refill anywhere, you need a new prescription.
If you need a new prescription, it is important you understand the situation appropriately so you can relay that information to the doctor. Communication is key. If the pharmacy made a mistake, it may be an option to have them contact the prescriber.
Additionally, North Carolina has a database that maintains a fill log of controlled substances for patients. The database is called the 'North Carolina Controlled Substance Reporting System'. If your doctor is concerned about drug abuse and diversion, they can verify your fill history on that database.