Confederate infantry didn't arrive outside Columbia until Nov. 26th. I'm not sure that's enough time for a soldier to be wounded, transported close to a hundred miles southwest to Corinth MS and die by Nov. 29th.

David Pearson may simply have become ill on the march west to Florence AL. It's also possible that he had been wounded in the fighting at Decatur AL in late October or in the skirmishes along Shoal Creek AL in mid-November. Either way, he would've been sent to a recently-established hospital on the Mobile & Ohio rail line at Corinth MS. During this period Confederates engineers tried to repair the Memphis & Charleston line between Corinth and Tuscumbia/Florence but never completed the work.

http://en.wikipedia.org/wiki/Franklin-Nashville_Campaign