What North said. Truck should tell you if tire pressure is low but wheel balance, lugs, or some other thing needs to be checked manually. If your dealership is cool they should be able to inspect it for free. Cant imagine the bed shaking that badly since F150s have very solid frames.
OP - You live in Canada? Could be that crazy maple leaf snow!
Also let us know the root cause. I hate reading problem threads with no solution!