See Statute 130A-118:
"A written request from an individual is received by the State Registrar to change the sex on that individual's birth record because of sex reassignment surgery, if the request is accompanied by a notarized statement from the physician who performed the sex reassignment surgery or from a physician licensed to practice medicine who has examined the individual and can certify that the person has undergone sex reassignment surgery."
North Carolina will then issue a new birth certificate.
Contact NC Vital Records to order a new birth certificate. You can have your name changed simultaneously if you already have your court order for name change. There will be a fee for processing and issuance of a new birth certificate.