Hi Harriette,
My 4x ggrandfather, William Ewing b. 1790, was from County Tyrone, but I am not sure where. I'll second Karen Avery's suggestions to visit the Ewing Family website and, if a living male Ewing is willing, to have a Y-DNA test performed. I've done one myself and am still hoping for close matches for someone with a Tyrone background.
Good luck and regards,
Mike Ewing