Dear Doyle,
Unfortunately, the roster that I have of the 28th Texas does not list the place or date of death of soldiers. I did find a newspaper listing of men who died in the 28th Texas from October-December 1862. However, that time period is outside of the one that you mention.
I do have ideas on places that you can search for additional information--you may have already delved into some or all of these.
There are two background articles about medicine in the Trans-Mississippi that I found helpful when writing my book. These articles might contain some ideas on records to search through. These articles are:
Wilson, J. Woodfin, Jr. ³Civil War Medicine in North Louisiana.² North Louisiana Historical Association Journal, Vol. 17, no. 2-3 (1986): 58-64.
Wilson, J. Woodfin, Jr. ³Some Aspects of Medical Services in the Trans-Mississippi Department of the Confederate States of America, 1862-1865.² North Louisiana Historical Association Journal, Vol. 12, no. 4 (1981): 123-146.
Also the following book contains much material on a number of topics including some information about medical care. The book is:
Kerby, Robert L. Kirby Smithıs Confederacy: The Trans-Mississippi South, 1863-1865. New York: Columbia University Press, 1972. (this has been reprinted by the University of Alabama Press)
I have discovered that newspapers are a rich source of information. Occasionally, lists of men who had died of disease (along with battle casualties) were published in newspapers. Research libraries (such as the University of North Texas, the University of Texas at Austin, etc.) typically have collections of newspapers on microfilm. Although it would take a great deal of tedious searching, you would probably find some lists of men who died in Arkansas. Keep in mind that such lists often appeared weeks and even months after the death of soldiers--you might have to search newspapers for all of 1863.
You should be able to obtain the articles and the book through interlibrary loan at your local library. You might also be able to obtain newspapers on microfilm through interlibrary loan.
Hope this helps! Let me know if you have any questions.