I can't imagine how anyone could put that together from information available.

Let's start with Moore's 2nd Texas Regiment. One of the best regiments to ever fight for the state, officers and men saw action at Shiloh, Corinth, Vicksburg and countless other battlefields. "Mustered out in February 1864" cannot apply to this command, which reorganized after Vicksburg and served until the war's end. It does apply to the 2nd Texas State Troops, which organized for six months service in the fall of 1863 and mustered out at Galveston in February 1864.

Asst. Surgeon A. K. Middleton served with the 2nd Texas State Troops during this six-month term. Here's his biography --
http://www.tshaonline.org/handbook/online/articles/MM/fmila.html

A review of National Archives records shows no one named Middleton serving with Moore's 2nd Texas Regiment. I don't find anyone else in Confederate service who could be the Marylander you named.