I found your post very interesting as for a number of years I have been researching and writing a book on the battle of Stone's River/Murfreesboro. When Bragg's army evacuated Murfreesboro, there were about 1,200 wounded left in the town. If Private Kirby was among those wounded, and he subsequently died as a result thereof, it is likely that he was buried at a Confederate cemetery just south of town on the Shelbyville Pike.
In the late 1860's the bodies were removed to Evergreen Cemetery in Murfreesboro. In the intervening years, the names on the wooden grave markers were erased by the elements so that only a few of the 2,000 could be identified. While the list of those identified as buried at the Confederate Circle does not include any members of the 10th South Carolina, it does bear the name of several men from the the 19th South Carolina Infantry, a sister regiment in Manigault's brigade. Interestingly, Colonel A. J. Lythgoe, commander of the 19th South Carolina, who was mortally wounded in the battle, is buried there. His name is given as "Lithgood."
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Best Regards & GOD's Blessing,
L. K. Smith