Did you choose to have TT fees deducted from your Federal refund? (Remember that if you did that, you also agreed to an extra refund processing fee of $39.99)
How can I see my TurboTax fees? https://ttlc.intuit.com/questions/2565973
And the fed & state returns are sent separately from different taxing authorities ... so when you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. what does it say?
Was it Accepted? You can check your efile status here https://turbotax.intuit.com/tax-tools/efile-status-lookup/ What does the state say? Check for a state refund https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund Make sure you are using the refund amount from your actual state tax return and not the combined amount Turbo Tax showed you at the end. That was for federal and state combined.
Per NC:
Due to enhanced identity theft protection measures, some refunds may take longer than normal, which is 8 weeks for electronically filed returns and 12 weeks for paper returns.
https://eservices.dor.nc.gov/wheresmyrefund/SelectionServlet