I'm looking for IP addresses that were used with my account.
You can't check this information and it isn't really confirmatory evidence.
Yesterday I see some messages in my email that are not in my inbox.
Today user accused me of stealing the money from him, even though I was offline.
If your email nor password has changed, then it is not easy to tell/prove this. If there have been outgoing messages that you did not sent, then it is highly likely that someone else logged into your account at some point. Change your password.