When you enable POP, all messages are downloaded to your client, except for Spam, Trash, and Chats. If you don't want messages that you send from the web interface downloaded to your mail client's inbox, we suggest creating a filter within your client. You may want to contact your mail client's customer service department for instructions on how to categorize downloaded messages.
If you receive in your inbox a copy of messages sent from your BlackBerry device, see this article.