Does anyone know where the wounded from Shilo were cared for after the battle and later on?

Lt Col John B Thompson of the 1st Ark Inf wounded 26th (his birthday), died 28th. Margaret Ross wrote in 1950 that Capt Thomas W Newton, Jr laid next to him as he died, and I assume that to have been in an area where wounded were kept after battle for as Bryon Howerton pointed out, they were in different outfits, not fighting in same area, so she errored, ---- but they could well have been together in a hospital area when Thompson died?

I've read also some injured were taken to Little Rock's St Johns' College (which I'm researching as a school) which had become a hospital? Is there any documentation?