Allmusic.com says there are 3 CDs by Winifred Atwell that contain WAY UP IN NORTH CAROLINA.
"Let's Have a Party" (2005)
"Honky Tonk Boogie" (2005)
"Winifred Atwell & Her Other Piano" (2005)

I assume these are reissues of older recordings.

Winifred Atwell is mainly known as a pianist, although she did sing sometimes. I don't know whether she sang on this particular recording.

I haven't found any lyrics or sound files.

Of course it's possible that there is more than one song with the same title, so I can't guarantee than any of these are what you want.