I can't add much, but I do find a little more than you have in your post.

Capt. Tappan Wright Kelly/Kelley's company was Company D of the 1st Regiment Maryland Cavalry, Potomac Home Brigade (Union). Prior to that, his company was Company M of the 2nd Regiment Maryland Cavalry (6 months, 1863-1864). I don't find any info prior to those dates.