Cherokee Springs Hospital appears to have been in Catoosa County, GA,
the county seat being Ringgold.

I've not done research at the public library in Ringgold, but I understand it has
a nice history & genealogy department.

Here's an email address for their archivist, Connie Haney:

conniehaney@catoosacountylibrary.org

If you don't get a response, you might want to call the librarian or drop
them a letter of inquiry.

Sincerely,

Greg