NPS-CWS&SS shows a "Thomas Kelly" in the 2nd Battalion, Virginia Infantry, Local Defense (Waller's), (Quartermaster Battalion) and 2nd Regiment, Virginia Infantry, Local Defense, but I don't see one in the 3rd Virginia Infantry.

I do show a "Thomas C. Kelly" as:

Thomas C. Kelly
Regiment Name 34th Virginia Infantry
Side Confederate
Company K
Soldier's Rank_In Private
Soldier's Rank_Out Private
Alternate Name Thomas C./Kelley
Film Number M382 roll 31

34th Regiment, Virginia Infantry
34th Infantry Regiment was organized in May, 1862, with men from Norfolk, Richmond, and Yorktown, and the counties of Gloucester, Mecklenburg, Bedford, Greene, and King and Queen. For almost two years the unit served as heavy artillery attached to the Department of Richmond and was known as the 4th Heavy Artillery. In May, 1864, it was assigned to Wise's Brigade as infantry. It participated in the long Petersburg siege south of the James River and saw action in various conflicts around Appomattox. It contained 466 effectives in June, 1862, and surrendered 14 officers and 210 men. The field officers were Colonel John T. Goode, Lieutenant Colonel Randolph Harrison, and Major John R. Bagby.

Also shown as:

Thomas B. Kelly
Regiment Name 34th Virginia Infantry
Side Confederate
Company K
Soldier's Rank_In Private
Soldier's Rank_Out Private
Alternate Name Thomas C./Kelley
Film Number M382 roll 31