Overnight, I've received 114 emails telling me that something I have sent is undeliverable. I haven't sent anything and nothing is showing in my Sent box.
sounds like mail spam. You're email has been used to send spam out to many thousands of other email addresses. The mail spam program 'guesses' email addresses of possbile recipients.
The 114 emails have bounced back from non-existant email addresses.
As Booldawg has suggested, your email address has been 'borrowed' by a spammer sending out mail to random addresses and entered into the 'return address' field of his spam.