Edmund's nickname Crouchback, is thought to be derived from the black cross he wore on his back during his time in the Crusades. However, his second son Henry of Lancaster, also went by a nick name that of Wryneck (the same name as a bird who can turn its head almost 180 degrees.) This condition we know now of as Torticollis, where the muscles of the neck cause the head to twist to one side.
Although there seems to be no evidence of Edmund having any physical deformity, I wonder if there was a history of spinal problems within the family, maybe Edmund did have a problem, but it was less noticeable than Henry's.
Edmund's remains were brought back to England and interred alongside his first wife in Westminster Abbey where his tomb features an effigy in armour with crossed legs and a series of weepers holding shields of arms are shown around the base.