You sure it's your inbox and not your outbox? Mine fills up all the time and i have to go and delete the outgoing messages or the same message pops up. I'm pretty sure it's your outbox as you can have 40 messages in your inbox.
Just look up the top of your messages page and you will see outbox there, click on that then you have the option of deleting them all(check all) or just the one's you dont want to save.
Darryl.