Yes. You are living in North Carolina, so you owe taxes to North Carolina. North Carolina taxes pension income from all sources.
You probably do not owe taxes to Georgia on this income.
On Jan. 10, 1996, Congress enacted the Pension Source Tax Act of 1996 (P.L. 104-94). This law specifically stipulates that, "No State may impose an income tax on any retirement income of an individual who is not a resident or domiciliary of such State." The Source Tax law prohibits any state from taxing non-residents for pensions earned within the state.
