The 4th AL Cavalry again! There were a ton of them, easy to get lost in the "forest" of 4ths. There was, however, a Forrest's Cavalry Regiment, aka the 4th Alabama Cavalry. It was organized with Julian's Cavalry Battalion as a core on or about 1 June 63. Then it was broken up when 4 Tennessee companies were transferred to the 18th TN Cavalry, four Alabama companies went to Warren's Cavalry Battalion, and another Alabama company went to Morelands Cavalry Battalion on 11 July 64. Incidentally, Forrest's Regiment was commanded by Jeffrey Forrest, not Nathan Bedford. Unfortunately, the dates do not correspond with your enlistment date.

Further muddying the waters, there was a Confederate unit called Forrest's Scouts. Therein is listed an "A. Sims" who could (might?) be your Alexander. Seems to me it would be easy to confuse all these names/numbers in one's memory over the years. I did not find a listing for Alexander Sims in Love's 4th Cavalry Battalion, or Roddey's or Russell's 4th Cavalry Regiment.