push something (up) against someone or something
to press something against someone or something. I pushed the chair up against the door to prevent the robber from getting in. Accidentally, I pushed the door against Donna and hurt her sore elbow.
push (up) against someone or something
to put pressure on someone or something. The small dog pushed up against me, wagging its tail. Push up against the ceiling tile while I try to tack it back in place.