As already stated, this isn't malware, especially since you say your phone is not jailbroken. As to what it is, there are several possible explanations here:
Someone is sending messages from my e-mail address!
This is written from a Mac-centric point of view, but is still applicable.
As to how the content of your Notes application is ending up in those e-mails, I'm not sure. Do you sync that phone to a Windows PC? If so, that Windows machine might be infected with some kind of malware. If not, is the e-mail address in question an iCloud e-mail address? (Any address ending in @mac.com, @me.com or @icloud.com would qualify.) If so, most likely the iCloud account has been hacked, which would give the hackers access to not only your e-mail address but all your notes, contacts, calendars, iWork documents uploaded to iCloud, etc.