My iPhone 5c won't let me unlock it or turn it off?

My iPhone 5c won't let me slide it so it will unlock and i tried turning it off but i couldn't slide it so it would go off and i can't press cancel but i don't think the touch is broken cause i can slide those things at the bottom that can allow me to turn brightness up or down but then it won't let me actually touch anything. Is my iPhone screwed or what?

Hold down button and lock button until the apple logo comes on then leave it this should work