George, this appears to be your soldier. The information was found using the Nationwide Gravesite Locator which I sometimes use. It's run by the National Cemetery Administration from what I recall. Tylertown is located in Walthall County, Mississippi not too far from where he enlisted. The phone number is listed below and perhaps you can gain additional information. I would not think there were too many Mississippi soldiers with the name of Richard B. Pittman who died on September 20, 1863.

PITTMAN, RICHARD B
PVT CONFEDERATE STATES ARMY
DATE OF BIRTH: 07/27/1828
DATE OF DEATH: 09/20/1863
BURIED AT:
THOMAS CEMETERY
PRESTON STOGNER RD TYLERTOWN, MS 39667
(985) 839-2206