Albert Ballard, Co. "F", 16th Tennessee Regiment, had been assigned to care for sick and wounded soldiers during the Battle of Murfreesboro TN. He was captured when the town fell into enemy hands but returned from prison and rejoined his command a few months later. Albert died of typhoid fever at Fairgrounds Hospital No. 2, Atlanta GA, May 28, 1864.

Carroll Ballard, Co. "F", 16th Tennessee Regiment, was wounded during the Battle of Murfreesboro TN, Dec. 31, 1862. However, he survived the war to take the oath of allegiance at Chattanooga TN, May 5, 1865.

Joseph Ballard, Co. "F", 16th Tennessee Regiment, was indeed killed during the Battle of Murfreesboro TN, Dec. 31, 1862. However, since Joseph Ballard was age 23 on the date of enlistment in 1861, he would be twelve years older than the Joseph Ballard you have in mind. Since your Joseph Ballard would have just turned fifteen when the war ended, we would not expect to find any military record for him, at least not during the Civil War.

Copies of all three service files are available here.