I was wondering if you were researching hospitals in Tennessee only. I run across info while trying to research soldiers (especially where they died and are buried). The cemetery at the Middlebrook Pike plantation in Knoxville has been one of those that I have tried to find a listing of the burials. Even went to Knoxville to the East TN Historical Society library.
Thinking about the Middlebrook plantation, I looked up and found some info on hospitals in Knoxville from the Knoxville News Sentinel newspaper April 2012.

1. Fairgrounds east of downtown in the Shieldstown community early in the war by CSA
2. Dr. Harvey Baker treated wounded CSA at his home west of Knoxville (now known as the Baker-Peters House)
3. Middlebrook house and paper mill owned by Gideon Morgan Hazen used 1863 after Battle Ft. Sanders
4001 Middlebrook Pike (house/cemetery); paper mill near Third Creek
4. TN Deaf and Dumb Asylum (called Asylum Hospital) Western Ave & Broadway (USA & CSA)
5. Knox County Courthouse, Main St.
6. Numerous buildings on the UT (East TN Univ. war time) campus (USA & CSA)
7. 17 houses in the city
8. Lamar House Hotel, Gay St.
9. Bell House Hotel
10. East TN Female Institute, Henley & Main
11. USA used the churches:
First Presbyterian, 610-620 State St.
Second Presbyterian
Church St. United Methodist
First Baptist
12. Hospital tents on south side of Holston River July 1864
13. Holston USA General Hospital; 1000 beds; Dr. John Shrady in charge
14. Wayne Wallace's house near Locust St. & Cumberland Ave (8 CSA)
15.Campbell Station Inn, 11409 Kingston Pike, Farragut (owned by the Russell family and used as hospital for the
wounded from Battle of Campbell's Station
16. Campbell-Nelson-Russell house, Farragut (owned by Dr. William Nelson; treated wounded from Battle of Campbell's
Station

Also, I found a site www.pa-roots.com/pacw/hospitals/hospitallist.htm that lists USA hospitals in different states

Hope this is helpful to you and others.