Here are some bits and pieces I found by googling over my morning coffee:

The Gayoso hospital was a U. S. General Hospital. The National Archives may have some records from the hospital.

Gayoso was a Bayou, and some TN regiments were assigned to
"guarding the bridges on Gayoso Bayou from Monroe Street north to the Mississippi River...".

"The Gayoso Guards." Men from Memphis. 2nd Co. "K"., reorganized; originally "G", 42nd Tennessee.

Article about the decision to use the "Gayoso Block" as a U. S. general hospital:

http://www.tennessee.civilwarsourcebook.com/collection/1863-03/1863-03-Article-54-Page95.pdf