Stop Receiving Emails from GMail Sent Items In BlackBerry Inbox

Every time you send an email from BlackBerry, a copy of that email arrives back in your inbox. That’s because the mail you just sent is saved in the Sent Items folder (of GMail or Microsoft Outlook) and BlackBerry probably confuses that with a new email.
To fix this, open your BlackBerry Internet Services portal (like airtel.blackberry.com or vodafone.airtel.com), login and create a new filter.

Filter Name: Block Sent Items
Apply Filter When: "From" field
Contains: myemail@xyz.com
Now check "Do not forward messages to device" and click Save. Exist the BIS website and your own email won’t reach your BlackBerry again.
If you are on Microsoft Exchange server, you may disable the synchronization of Sent Items folders (that contains your emails sent from the Exchange mailbox) via BlackBerry itself.