Hello. Any time I hear the words Texas soldiers and died in Arkansas, the first thing I think of is Camp Nelson.
It is possible that he is buried at Camp Nelson which is sort of north east of Little Rock. (Camp Nelson is well kept is my understanding.) It is where the Texas soldiers made camp and where lots of them took sick and died. Supposedly it was so bad that it was hard to even bury them as the others were nearly dead themselves.
As far as the hospital being in Little Rock, the person may have meant near Little Rock. It is possible that Camp Nelson was in Pulaski County at one time as all the lines have shifted since back then.
No matter where he was, he was not taken far, not with Typhoid fever or any other highly easy to catch disease, so no he did not make it back to Texas.
If I were you, I would run a search for Camp Nelson which is now in Lonoke County to see what it says.
This is not probably what you were hoping for, but it might be the best you get.
Good luck.
Linda