Some users have a workflow that includes sending emails to themselves and they want those messages to show up in their inbox. By default Gmail automatically marks emails from self as read and only lists them in the Sent mail folder. Google is often altering the way their email works, and this can be challenging or even out of date.
Set Up
In Gmail -> Gear menu -> Settings -> Accounts tab find the Send mail as: section and click the "Add another email address you own" link.
Add the user's "myname@u.washington.edu" address here. Leave Treat as an alias CHECKED.
Gmail will send a confirmation email (since myname@u.washington.edu is an alias it will just go to the user's inbox). When you get that message click the link in it to authorize sending as that address.
How to CC Self
Once the second address is configured as an alias user can CC their myname@u.washington.edu address and those messages will go to their inbox marked as unread.