My sent emails show in my inbox on my iPad. I have looked but "always bcc myself" is not checked. This problem has started only recently, but I am not aware of anything I may have done to start it. It doesn't happen when I send emails from my Mac computer using the same account.
Are you sending yourelf a bcc: of all mail?
Check your: settings > mail, contacts, calendar > always bcc myself
See if that slider is turned on.
If you're using imap, you might be storing sent mail on the server.
If you uncheck that, you won't see the emails on your other devices, because you won't be keeping a copy on the server. (You will have the copy on your local machine)