Janice --
The hospital had long since been moved to Shelby Springs, Ala. The hospital card says Jackson Miss. -- how would you be expected to know otherwise? There is a hospital cemetery at Shelby Springs and at least one article has been published about the hospital.
Here's a link to a rather long, detailed description of Shelby Springs, at one time a popular resort site. If you use the link at the bottom of the page cited below, you'll find a list of marked graves.
Russell McClain, Co. "C", 6th Alabama Cavalry, is one of them:
http://www.rootsweb.com/~alshelby/ShelbySprings.html