My sister put kitty litter down the toilet

So my sister flushed our house cat’s kitty litter down the toilet about a year ago (stupid decision, I know, we already lectured her for it) and ever since our toilet has to be flushed multiple times to go down, and we have been experiencing flooding sinks and plumbing issues in our other bathrooms as well as in the kitchen sink.

I live in a house full of girls and we don’t have the money to afford a plumber. I want to know if I can stick a toilet snake down the pipes and if that will help.

Can someone give us tips on how to maybe fix this?