There was no 19th army during the war. Union Armies were generally name for rivers, Potomac, Ohio, Cumerland, Tennessee, etc. Confederate Armies were named for the geographic area to which it was assigned. Army of Northern VA, Trans-Mississippi, the Tennessee, etc.
The 19th OVI were actually two in number, a 90 regiment and a three year regiment. Neither saw duty in LA although the 19th was stationed in TX for a short time at the end of the war as part of the XIVth Corps and may have paqssed through that state. http://en.wikipedia.org/wiki/19th_Ohio_Infantry