I just logged into my ex-girlfriends facebook-account
Wow, there are so many things that could go wrong.  How did you log into her account?
I just guessed her password.
There could be legal ramifications as well as ethical issues with logging into someone else's Facebook account without their permission.  Please come clean to your ex-girlfriend so she can change her password for security.
Oh, it's fine. I'm seeing someone new so I just want to make sure she's not doing the same stuff she did with me.
While it's great that you want to protect future boyfriends of hers, it's not your responsibility anymore.  She has a right to her privacy, just as you have a right to yours.