Many major railroad depot in the South have Confederate cemteries, located nearby the main hospital. Covington isn't found on the Lynchburg Confederate Cemetery list, but two other men from the 13th Mississippi Regt are there. Both died about the same time as Covington, and their death certificates were processed on the same date (Feb 1, 1862). More here --
http://www.gravegarden.org/confedsection.htm