It depends. You must file your return in your State of legal Residence (SLR). You may elect Tennessee as your State of legal Residence if Tennessee is considered your permanent legal residence, as demonstrated by a wide variety of factors that include:
Your legal residence as shown by these factors should be the same place as your legal residence indicated on your Leave and Earnings Statement.
If you registered to vote in NC, maintain a driver's license, register vehicles in the state, then your State of legal Residence is North Carolina.
If you have lived in NC since leaving active duty with the intent of making it your new, main home (your domicile in tax terminology), then for tax purposes your State of Residence is now NC.
According to this reference, NC does not tax military pensions, including medical retirement.
https://ourncmilitary.nc.gov/blog/2022/02/25/military-pension-tax-exemption