Deb,
There is a man listed in the Broadfoot's Confederate Roster by the name of James Alvis. He is listed as being a member of Carrington's Company which was a part of Gidding's Battalion. According to Texas in the War 1861-1865 edited by Col. Simpson ; Giddings' Texas Cavalry Battalion served along the lower Rio Grande and participated in the last battle of the Civil War at Palmito Ranch May 13, 1865. May not be your man but he is a possible.
Regards,
Charlie P.