First, don't be panic. It could be solved. Turn off the hacked email page.
Second, In addition to the email address, the mail subject field etc could be hacked too. This could happen when you use php mail() but didn't check the header such as "subject", sender etc. For phpmailer, you need to check to see if "email header injection" is already checked and blocked or you need to do so by yourself.
Also, check the bad emails, and you will find out which exact script was attacked. Make sure that the script attacked is the one you think it is.
Search for "email header injection" and php. You will find the answer and solutions.
Basically, valid these mail headers values if you get these values from the client.
If it is not the "mail header injection" attack, then do more research and ask around here with your codes (but be careful not give out yourself to more attacks.")
Third, after you fixed the security holes and then turn back the script.
Fourth, as for the bad emails already, it depends on your server manager. Due to there might be many good emails in the mail queue. They may not be able to clean the mail queue out for you. If it is not too serious or too late, after you fix your hacked php page, the mail queue should clean up in 3-4 days or so.
Fifth, check your other scripts on this server, to see if there are same security holes. The hackers may try to get in again.