Sallie Witherspoon was the daughter of James H. Witherspoon. There was also a 4th son living within the family of Kate Till and he was 16 in 1860.
Not that it would do you much good but I've compiled by county and Post Office those who died at Camp Chase. When I looked for Lauderdale County, Alabama I saw one for Company H of the 4th Alabama Cavalry with the Post Office being Waterloo.
It appears the 4th Alabama Cavalry was created well after May of 1861.
It is plausible that who ever this mystery company was they could have reorganized or have been disbanded.
I saw nothing in the Alabama Department of History and Archives but have not checked the same for Mississippi.
Stick with it Greg sooner or later you probably will have some luck.
George Martin may also have some valid points.........................