Apartment troubles. What should we do?

We have been having this problem for quite a while now. We live in an apartment complex. Its called Bonnie Ridge and every building has six apartments. There are three floors and we are on the 1st floor. Sometimes our toilet has problems and starts spouting out water. When we call the maintenance they always found stuff jammed in there that we never threw. Problem is, they don't believe us. Their mindset is if it came out of our toilet it must be our stuff. Now it's gotten worse. Today the toilet got blocked again and there was water all over the floor. The plumber found tampons, lipstick, and what looks like baby toys. He says they will charge us. They don't believe its not us. We do suspect the people upstairs. They have a 3 year old daughter who might have thrown in the baby toys and lipstick. My mom doesn't use tampons so thats not ours either. Just on a sidenote, the people upstairs are wacko. I mean like they yell and scream at each other and run around the apartment in the middle of the night. But that's not the point. What do you think we should do? It's clearly not our fault we should not be charged for something we haven't done. Please help.