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.
Depicted below is a 14th century image of a knight, thought to be Edmund with Saint George, taken from a manuscript held at Oxford's Bodleian Library.