The papers of Dr. Samuel H. Stout may have the records. This collection has letters, hospital records, and military papers documenting his career as Confederate Medical Director of Hospitals, Army of Tennessee.
Those records that survived have been broken up and sold off by the family over the years but the majority of them are likely at the Center for American History at the University of Texas at Austin.
You may want to also refer to "Confederate Hospitals on the Move: Samuel H. Stout and the Army of Tennessee" by Glenna R. Schroeder-Lein.
You also may want to look at the soldiers Compiled Military Service Record. If he has a "card" in his record that refers to his hospitalization then that was taken from a hospital records/roster. That would likely be on microfilm at the National Archives in Washington, D.C.
I hope this helps.
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment