I cannot help you on his New Orleans prison stay, try this query on The Civil War Prisons Message Board

There is one undated card in his file of the 21st which states that his name “Appears on a Register of sick and wounded prisoners of war at City Hospital, Mobile, Ala. Complaint - Wounded”

He also appears on another undated List of sick and wounded, C. S. A., in City Hospital at Mobile, Ala. There is nothing written under the entry for Remarks

There are also Receipt Rolls for clothing dated March 3, 1864, June 1, 1864, and March 31, 1864, Signature “By mark”

……

J. D. Haynes, Private, Company L, 3rd Alabama Infantry, admitted Episcopal Church Hospital, Williamsburg, Va. May 10/16, 1862, Rubeola, returned to duty June 12, discharged for disability July 29, 1862, no further records

Note, his Certificate of Disability for Discharge is unreadable on line except this statement: “I don’t think this man will ever be capable of performing the duties of a soldier.”

M311: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Alabama

Unfortunately there are no Company muster roll records in either file, without these, we cannot ascertain his initial entry into service of either of these units.