Getting delivery failure emails for messages I never sent

Open one of the bounces and look at the copy of the original message attached to it. Most of the time it's backscatter - a spammer forged your address as the sender, the receiving server rejected it and bounced it back to you. Annoying but harmless, and there's not much you can do except wait it out. If the message is also sitting in your own Sent folder though, that's a different story: someone is in the account. Change the password, turn on 2-step, and check filters and forwarding rules for anything you didn't add.