I find nothing in the literature to indicate he was the first to die.

Thomas J. Teernon
Enlisted as a Private
"C" Co. MS 10th Infantry

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records

…………..

Thomas J. Teernon, age 24, Private, Captain Wm. McKeever’s Company (Port Gibson Rifles), Mississippi Vols.*, enlisted March 28,1861 at Port Gibson for one year, recorded on the Sep/Oct, 1861 muster roll as present, Capt. McKeener [sp?] recommends a discharge on the grounds that he is unfit for a soldier, recorded present at the end of year muster, no further records

* This company subsequently became (Old) Company C, 10th Mississippi Infantry

M269: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi