I would believe you have no choice, albeit absence of other evidence, that he was buried in the Okolona cemetery with the others who died at the hospital.
This description indicates that approximately half of the 800 or so who perished at the facility were never identified. See: Confederate Cemetery - Okolona, MS.
Unless he came from a family of means, it is rather doubtful that his remains were later brought home.
You might find a Goggle search “okolona ms confederate cemetery” to be helpful.. Also, contacting local authorities and also the nearest SCV Camp should provide additional historical information.