Joe,
The Mississippi Department of Archives & History has the following history of the unit, which covers their history up through the siege of Vicksburg:
“Sketch History of the 7th Mississippi Battalion.” No author, no date. J. L. Power
Collection, Box 8, Catalog # Z/0100.000, Mississippi Department of Archives and History, Jackson, MS.
The author is unidentified, but having read the history, I believe the manuscript was written some time after the war by a member of the 7th Mississippi Battalion.
I hope this helps,
Jeff