Do you have a Tennessee concealed carry permit?

Elsewhere you will find that concealed weapons are allowed, and NC does have a reciprocal agreement with NC. Here's a link and the specifics are shown below. Park Rules | NC State Parks

Firearms and other weapons are prohibited except that those with a proper permit may possess a concealed handgun in permitted areas and under the requirements of North Carolina G.S. 14-415.11. All firearms and weapons are prohibited in state park visitor centers and park offices. (EXCEPTION: Federal law (36 C.F.R. § 327.13) prohibits loaded firearms or ammunition on those lands and waters at Falls Lake, Jordan Lake and Kerr Lake state recreation areas managed by the state parks system and owned by the U.S. Army Corps of Engineers.)

Fireworks, cap pistols, air guns, bows and arrows, slingshots and lethal projectiles or missiles of any kind are prohibited on all properties managed by the N.C. Division of Parks and Recreation.

Here's a link to GS 14-415.11. Nothing unusual there. It also references the following:

(c1) Any person who has a concealed handgun permit may carry a concealed handgun on the grounds or waters of a park within the State Parks System as defined in G.S. 143B-135.44.

That reference just describes what a state park includes. If you have a Concealed Carry Permit, you're probably OK.