Mr Dye,

In a real quick look this morning, the only Henry Dye I find is a Pvt in Morgan's Texas Cav., probably not your man . There is another Henry Dye from Georgia , but, he too is a Pvt in an infantry regiment.... not your man either. I dont' find your man in an Arkansas outfit either , ( yes, I remember he was from Texas) . I'll tell you what you might want to try if you haven't done it yet and that is post your inquirey on the Arkansas Civil War Board. There may be a researcher in Arkansas who really specializes in the CSA hospitals in Arkansas during the war. Do you know if he filed for a CSA pension later in life? If he did, that would provide you with leads on at least who he served with initially. From there , you may be able to track him down.
You know Medical Doctors ( Regimental Surgeons) often got left behind to care for the wounded when their unit was involved in a retrograde movement ( retreat!!) . Obviously, they got captured and at least until U.S. Grant stopped the practice, most of them were paroled / exchanged and returned to either their unit or another unit. Doctors were in such high demand that he may have started out with a line combat unit and ultimately been reassigned to a hospital like at Little Rock or Camden.
Another possibility is that he was not serving as a uniformed , commissioned officer MD but rather in a civilian capacity. That happened too.
Good Hunting , CAM