The 37th Alabama actually wintered in J.C. Moore's (old)-Alpheus Baker's Brigade at Dalton, Ga., following their retreat from Lookout Mountain/Missionary Ridge, and demonstrated under Col. Higley in the various actions near Dalton ("Buzzard's Roost," "Tunnel Hill," "Dug Gap," "Crow Valley") in late February 1864.
I believe the 37th Mississippi may have been part of Canty's Brigade at Mobile you're thinking of during roughly that same timeframe.
But, both regiments were in the fight at Iuka earlier in the war...