The name of the church converted to a hospital was the Brunswick Cumberland Presbyterian Church.
See TN Historical Marker 4E51. Tennessee Historical Marker 4E51 is for Pleasant Hill Cemetery in Brunswick, Tn. Reads :
"This cemetery, founded in 1853, grew up around the Brunswick Cumberland Presbyterian Church, which has since moved. During the Confederate War, the church building was used as a hospital, and 17 unknown Confederate soldiers who died there are buried in a nearby plot. Also buried there are many of the regions's pioneers."

The cemetery is Pleasant Hill Cemetery.

The marker does not contain specific dates. However, we know that Price fought at Pea Ridge and elsewhere in Arkansas, and, being transferred across the Mississippi, was present at the siege of Corinth. Special orders announced that the First brigade of Price's division would embark for Memphis April 8th, and Colonel Little would take command it can be concluded that the a part of the Army of the West was in Memphis at some point. If nothing else it would also be possible/probable these men were wounded at Corinth in April 1862 and evacuated to the hospitals in and around Memphis just to be moved again in June 1862.