My e-mail server is being used by spammers and getting my account blocked

My e-mail server is being used by spammers and getting my account blocked

A couple weeks ago, my account started being blocked over and over again because of the reason "rate limit exceeded", but I do not use my e-mail server to send mass mailings or spam messages. 

Last night, I received a message saying that dozens of emails were undeliverable. However, these were not e-mails that I sent, and I do not know any of the e-mail addresses on the undeliverable list. 

The majority of the errors say " INVALID_ADDRESS, ERROR_CODE :550, ERROR_CODE :Requested action not taken: mailbox unavailable".

I suspect somebody is using my server to send mass mailings/spam, which would explain why I keep exceeding the rate limit and getting blocked from sending messages.

How do I lock down my server to prevent others from using it so that I can stop being blocked from sending messages?