I suspect that the reference to the 13th Mississippi does not mean 13th Ms. Infantry.

The unit referred to as such is most likely a Mississippi Cavalry Unit.
Names and unit designations for these can very confusing.
A very brief search that I made shows no 13th Ms. Cavalry. The unit probably has a different designation.
If you wish to identify this Mississippi unit, and all else fails, perhaps the records of the First Alabama will help.

I can't be of much other assistance, but I wish you the best of luck.