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Email forging/spoofing, spam originating from one's own address, error messages in bulk
It's possible you may be receiving spam as if it had been sent by your own address. Rest assured: you, and only you are receiving this spam coming from your own email address. This spam isn't being sent from your own address to people in your contacts list. The integrity of your email account has not been jeopardized at any time.
To reduce the amount of these messages in your inbox, check if your own email address is present in your spam filter's whitelist (In your Webmail, under Mail settings -> Security tab -> "Managing the whitelist" button, and then select your own address and delete it using the "Trash" button. You may of course set it back once the wave of spam has stopped).
If you're receiving error messages indicating non-delivery of spam messages, here again, it isn't truly a matter of messages being sent from your account, but messages that pretend to come from your address. Indeed, anyone can pretend to be you. Anyone can use your email address as the sender, in the same way that anyone who sends mail by traditional means can indicate your address at the back of the envelope, thus making the recipient believe that you are the sender.
Spammers (people who send vast amounts of commercial messages, on command) use all possible methods to bypass existing spam filters and reach their goals. One of these methods consists in modifying the sender's address of the messages they send (either by manufacturing them, or by randomly selecting them in existing lists) in order to avoid raising recipients' suspicions. It is therefore difficult to trace back the true source of the message as the name and email address shown are not the correct ones.
These messages are usually transmitted in one of two ways: either through a mail server that is poorly secured and that spammers have discovered and use the time the problem is recognized and resolved or by Trojans that have infected hundreds of thousands of PCs around the globe and send messages almost automatically, unknown even to those computer owners (zombies), upon the spammer's request (botnets principle).
This doesn't imply in any way that you have suffered any hacking of your account, an email address theft or identity theft; it's rather an attempt to defeat spam barriers. It's a nuisance against which we unfortunately cannot do anything. The only solution resides in the securing of all mail servers in the world, all servers requiring authentication to send emails, as do our servers. Unfortunately, as long as all servers are not secured, mail forging has a bright future ahead of it.
Check also whether you have a "catchall" address on your hosting from within the list of mail accounts. Cancel the possible redirection to your overloaded mailbox if necessary. Doing this will greatly reduce the return of undelivered mail.