Bryan,
You could be right. If so I'd have to guess that the hospital was at Brownsville Station just east of present day Lonoke.
Walker's Texas Division camped near the railroad for a short period before moving to Camp Bayou Metoe which was on the Bayou but several miles from the railroad according to Elijah Petty. He stated that they were in a low muddy area so moving the sick to a healthier locale would make sense. A few Confederate items have been found in the Brownsville Station vicinity - not enough to indicate a camp but a hospital wouldn't be out of the question.