You can. Not sure how you're reading options are set but if you go to the left hand column, under 'Messages', there are 3 options: 'New Message', 'Inbox' and 'Outbox'. That section is above the 'Preferances' section. Click on 'Outbox' and you'll see your sent messages.
Also, go into your 'Profile'. Again, in the left column, 2nd section, you will see one for 'Modify Profile'. Click it. You will get what looks like a message box except that it's an 'Ignore List'. Under that are 2 boxes you might want checked. The first one is to opt to save a copy of your PMs. Make sure that is checked. The 2nd allows a pop up window to display whenever you receive a PM. So, maybe you should first make sure that you have your save PMs box checked and then go check your 'Outbox'. Of course, if you didn't have it checked in the first place, you won't have any sent PMs to read until you actally send one.