Something's off, particularly if the bed wood is fitting OK in front.
It's best to do the assembly off the frame, then lift the whole box onto the frame but on or off, I'm assuming the box is bolted together and the cross sills are all in place. First, check to see that the rear cross sill is properly bolted into the rear stake pockets. The rear cross sill has a lip or shelf on the inner edge and the rear end of the bed board should fit down snugly, resting on the bottom of the lip and flush with the horizontal surface of the cross sill. If the front bed panel is properly bolted to the sides and to the #1 (frontmost)cross sill, and the rear cross sill is installed correctly, the bed boards on the extreme left and right sides should slide snugly under the bed side irons that are welded to the sides. In other words, you can't just drop them into place. They have to be placed on the sills closer to the center of the bed and then slid over into position uner those bed side irons. If this is a shortbed, the bed has wooden blocks and neoprene pads under only the #1 and #3 cross-sills. The rear cross sill uses only the little neoprene pad between the frame and the "ears" or brackets, where the bolts go down through.