To quote from Ken Noe: "Conditions in Perryville hospitals indeed were "nasty", and certainly grim enough to worsen an already bad situation. One recent study reveals the results. Deaths occurred during certain peak moments for various reasons related to health care. By October 11, most of the mortally wounded had expired, largely from severe wounds and loss of blood. Incomplete hospital records reveal thirty deaths on October 9, but only fourteen two days later. Then, over the next four days, deaths among slightly less injured men peaked at thirty-nine on October 15.... The death rate again fell off after the fifteenth so that by October 19th the most severely affected were dead. Only nine men died in Perryville that day. Once again, however, the cycle repeated, as delayed infections, notably pnemonia and peritonitis, set in. Twenty-two men died on October 20th." "As wounded Confederates expired, townspeople buried them in area cemeteries."
The fact that Needham is not listed among our records of area cemeteries, suggests to me that he was among the "walking wounded". By October 20th (i.e. delayed infections, pnemonia, etc.) the vanguard of Bragg's force was in Morristown, TN and the rear elements in the vicinity of Cumberlad Gap. Had Needham already become symptomatic by the 18th, he might have been dropped off, for care, as far north as Crab Orchard, KY.
I wish I could help more.