I have always been told that the Memphis newspapers ran articles telling people to go out and pick up their wounded.
My great grandfather, James Thomas Harper of the 5th Tenn was shot in the knee and survived. I would assume he went home for care as his family was at Jackson, Tenn. He was later wounded again, we think around Atlanta.
My gg grandfather Sgt. Jerimah D. Pearce of the 8th Arkansas sent word to his family in Mifflin, Tenn. someway. His brother took the wagon and drove over and picked him up. I was lucky enough to find that out in his widow's application for a pension. He was shot "through and through." Pearce was also one of a handful of men who served with the 8th that made it back after the war.
I have also heard stories of how the wounded and dying were put on trains and sent south to be cared for by whomever would take them in.
Even after all these years, I still feel for all those poor men and can appreciate their caregivers being so kind.
I question that the men from Shiloh would have been sent to Little Rock as the trip itself would have probably killed the men. I do not believe that possible because the lack of roads and a descent railroad to transport the men on.
In 1860, there were only 38 miles of railroad track in Arkansas is what I was told, I think. It could have been that they used it as a hospital ward after the men had recovered some but still needed more care and time to heal. Everything about it was tragic to say the least.
Good luck in your search.