Louise Whitaker Arnold and Burton Kenneth Carr, 3rd, were married yesterday in the Episcopal Church of the Epiphany.  The bride, daughter of Mrs. Robert Clark Laughlin and the late Lawrence Heffernan Arnold, attended Centenary Junior College and is a University of Washington graduate.  Carr, also a U. W. graduate and member of Beta Theta Pi Fraternity, is the son of Mrs. Bruce Barnes of Bellevue and Burton Kenneth Carr, Jr., of Dallas.