Hi Frieda,
I think Walker Carrington was a son of Thomas Carrington born 1762 (wife Nancy Kennedy), a son of John Carrington dec'd 1803 Orange Co NC. Thomas disappears from NC.
Thomas Carrington had two letters early 1720s awaiting at the Jackson TN PO in present day Madison Co which is adjacent Henderson and Carroll Co TN. Thomas' daughter Lively Carrington born c1783 married Sterling Harris. A younger Sterling Harris was living near Walker Carrington in Henderson Co TN 1840 (possibly a cousin). Walker's oldest known son was Thomas A. Carrington born 1828 died April 1858 Hempstead Co AR.
I haven't yet located what happened to Thomas Carrington after the 1720s.
Gary