1. To put constant forceful pressure on someone or something. People kept pushing against me from behind while I was trying to watch the show. I can't open the door because something on the other side is pushing against it.
2. To press, shove, or thrust someone or something in forcible contact with someone or something else. In this usage, a noun or pronoun is used between "push" and "against." The bully pushed Billy against the wall and threatened to steal his lunch money. Someone pushed a table against the door from the other side so no one could open it.
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.
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.