Get messages that were sent in the last 7 days (Applescript)
Yes, that's absolutely possible.  Here's an example using my IMAP mail account, the name of which I've redacted for personal privacy:

    tell application "Mail" to get the subject of ¬
        every message of mailbox "Sent" of ¬
        account "C*************.com" whose ¬
        date sent &gt; ((current date) - days * 3)


This returns a list containing the subjects of each mail message that I sent within the last 3 days.

To apply this to your specific situation, you create a command that resembles this:

    tell application "Mail" to repeat with myMessage in (the ¬
        messages of mailbox MySentMailbox of ¬
        account MyAccount whose ¬
        date sent &gt; ((current date) - days * 7))
            .
            .
            .
    end repeat