There is no contradiction in the Gospels. The humiliated flogged individual who was to be crucified person bore his own cross because he was beneath help; nobody normally would be able to help him.
Three English Gospels including John use the Hebrew-Aramaic name ‘Golgotha’, and add the explanation in Greek that this means ‘the place of a skull’. In English, Luke alone uses the word ‘Calvary’ which is taken from a later Latin word meaning skull, a translation of the Greek name ‘Cranion’ found in Luke. So it is only in the Gospel of Luke in the King James Version that we ever find Calvary. Yet isn’t it remarkable that that has become the popular and the well-known and the best-loved term for the place of a skull - derived from the Latin rather than the Greek ‘Cranion’ or the Hebrew-Aramaic ‘Golgotha’.