Of course the 1st Mississippi Hospital operated in Jackson until May of 1863. Shortly afterwards it was relocated to Shelby Springs, Ala. Even after the move, patient cards for Shelby Springs are still labeled as 1st Mississippi Hospital, Jackson Miss.
There were quite a few more than three Confederate hospitals located in Mississippi. French's Division Hospital in Enterprise, Miss., comes to mind, as well as the hospital in Lauderdale Springs, Miss. Until its evacuation, Corinth, Miss., was the site for several military hospitals. The same was true of Vicksburg until the garrison of that place surrendered.