Are you serious?
Can you prove you didn't make the purchases?
I would call the credit card company and explain ASAP. The sooner you go on record with them the better off you will be.
Logically speaking, it is impossible to prove a negative. Thus they have no way to prove they did not make the purchases (by the way this is something only my twisted mind has thought of but if you close an account with a 0 balance and there is a mistake andt he CC company says you owe them 800 dollars because you made charges, you cannot prove you did not make charges which would be a mess in court, but oh well I don't mean to ramble that comes naturally when you get senile like me!)
I agree though, best to do that, but this could turn into a huge can of worms. Might end up needing legal help if it gets bad enough (which hopefully it won't).