Sir,
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.
The surviving records of Confederate hospitals are few and far between. The first location you should check is the soldier's Compiled Military Service Record (CMSR). The "cards" (with the exception of original records in the record) refers to another original record that his name appears on. So, therefore, if Private Johnny Reb's name appears on a "card" then look down at the bottom it should give some numbers (usually Chapter, volume, page number) that point to where his name was taken from.
Some records have survived outside the National Archives. Many of the Army of Tennessee's medical administration records that did survive were thanks to the efforts of Surgeon Samuel H. Stout. A very good book on the subject is "Confederate Hospitals on the Move : Samuel H. Stout and the Army of Tennessee" by Glenna R. Schroeder-Lein, published 1994. One of Stout's daughters sold portions of the records to various collectors and archives over the years and they are pretty dispersed. Below are several known locations of records noted by the National Archives for Chattanooga Hospitals, however, there are a lot more Chattanooga Hospitals and this does not include the Catoosa Spring hospital. The book referenced above gives several locations of his records in the bibliography.
Those records that survived have been broken up and sold off by the Stout family over the years but the majority of them are likely at the Center for American History at the University of Texas at Austin.
Foard Hospital (Chattanooga): A register of patients, November 2, 1861-March 15, 1863 (one volume), is in the Texas Archives at the UT Library (S.H. Stout Collection)
Newsom Hospital (Chattanooga): A register of patients, July 26, 1862-July 14, 1863 (four volumes), The register for December 1862-January 8, 1863, includes a list of sick in wounded Federal prisoners received.
Smallpox Hospital (Chattanooga): Record Group 109 (National Archives), Orders and circular received, May 22-August 15, 1863 (Chapter VI, Volume 274, page 3-18).
I hope this helps.
Respectfully,
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment
http://39thgavolinfrgt.homestead.com/39thHomepage.html