Accidentally flushed a plastic cup, toilet's broken?! How to fix?

I want to start off by saying, I don't want to waste a ton of money on a plumber.

So there was this spider, and my friend had this great idea of flushing it down to toilet. So I caught it in a small plastic cup, which is exactly 7 oz, and I went to throw the spider in the toilet (yes, I'm an awful person, please don't lecture me...). My hand then slips, and the cup falls down with the spider. My friend already flushed the toilet, so the cup went down. I didn't grab it in time, and I saw it go down a significant amount.

The spider didn't go down, btw. I picked it up using a glass jar and freed it outside later. My conscience sorta got to me, and the toilet doesn't flush no more...

Anyways, my parents are pissed off at me for throwing a plastic cup in there. Apparently it would have been better if I used one of those paper cups, any input on this?

Also, my dad wants to call the plumber, and make me pay $200 bucks for the repair costs. He says the cup's probably stuck in the "U-tube" part of the toilet. Please help?!!