Debbye, taking a clue from the fact that your Hiram Beam was born in Cherokee County, Alabama, I checked out some Alabama regiments and found Hiram and Whitfield Beam in Co. A, 48th Alabama Infantry. This regiment served in Law's Brigade, Army of Northern Virginia -- a pretty famous outfit, so there are several on-line resources available.

If this is your Hiram Beam, it would mean that he didn't move to Arkansas until after the war. Might be worth checking out.