I hesitated to respond to this since I do not have a conclusive answer, but a few years ago I wrote a history of the 28th Texas Cavalry. There is no J. H. Oates listed in the compiled service records for the 28th Texas, however, there was a Stephen H. Oats [Oates] who served in Company A. I assume that is the soldier referred to by the military doctor. The 16 May 1864 issue of the "Houston Daily Telegraph" contained a Jenkins' Ferry casualty list for the 28th Texas. Stephen Oats was listed as having been severely wounded in the jaw at the battle. My records do not indicate whether or not Oats survived his wound. Who authored the journal that you referred to in your query?