I just got a spam message from myself! A message I sent was not deliverable, except I didn't send it! Is my computer compromised?

Chances are, probably not. The From: header is very easily faked; spammers commonly fake that header in order to bypass spam filters. It can result in you receiving spam that appears to come from yourself. It can also result in you receiving notices that a message "you" sent were not able to be delivered.

Delete the message and don't worry about it unless you notice your computer behaving in bizarre ways. (Having said that, it can't hurt to change your password.)