There is an Owen D Griffin listed on Footnote as belonging to Co I, Youngs Texas Cavalry Regt. (11th Texas Cavalry), only one record and that shows enlistment at Camp Reeves on 2 Oct 1861 and that he deserted on 7 Oct 1861.
Is it possible that he served in the 5th or 6 th La Cav under another name? Applications for pensions usually required confirmation of Confederate sevice by fellow soldiers, if you can find those names and locate them in the 5th/6th it might help you narrow down the search.
Alan Thrower