"The Thigpen Tribe" states that Dr. Wyatt was an officer in the Confederate medical corps during the Civil War.  He is not listed in the 1860 Census of Turnerville, Lauderdale County, Mississippi, which may indicate that he had already left for the battlefields.
 

1860 Census, p. 145, Post Office: Turnerville, 20 Sep 1860
947/952  Rebecca Wyatt, 37, female, Farmer,
Real Estate $7,000   Personal Property  $2,000
Born Mississippi, can't read/write

T. C. Wyatt, 15, male, day laborer, b. Miss.

S. A. Wyatt, 13, female, b. Miss.  Attended school.

R. N. Wyatt, 6, female, b. Miss.  Attended school.

J. E. Wyatt, 11, male, b. Miss.  Attended school.

M. W. Wyatt, 4, female, b. Miss.

L. J. Wyatt, 2, female, b. Miss.

T. J. Mitchell, 22, male, farmer, $150 personal property, b. Georgia, can't read/write.

(Was T. J. Mitchell perhaps a laborer hired to help out while Dr. Tom was gone to war?)