Roster of Union Soldiers, 1861-1865, shows:

Dixon, Thomas (Thomas H. or Thomas J.) KY 9th Inf. Co.I
Dixon, Thomas KY 22nd Inf. Co.G Cpl.

I would say that the Thomas in 9th KY Inf is not yours. The Thomas in 22nd KY Inf is more promising.

22nd KY Inf [US] organized ar Camp Swigert, Greenup County, 12/12/1861 - Co 'G' was from Carter & Boyd Counties - Veteranized at Baton Rouge in March 1864 - consolidated with 7th KY [US] Veteran Inf - non-veteransa mustered out at Louisville, KY 01/20/1865 - veterans [now with 7th KY] mustered out at Baton Rouge 05/10/1866 & discharge at Louisville, KY

The Union Army, Vol IV, pages 333-334, 322