The American Civil War Research Database lists this soldier's name as Charles H. Fox, while the medical case in
The Medical and Surgical History of the War of the Rebellion lists it as C. W. Fox. Other details in these records (i.e., regimental information, date of injury, age) indicate that these sources refer to the same soldier.
Fox's birth date range is calculated based on his age at time of enlistment. Fox was 18 years old when he enlisted on 29 August 1864.