You can view a list of all the messages that you have sent or received through the events management system by going to your 'My Details' page under the 'People' section, and then clicking 'Messages sent & recieved' from the 'Select an Action' dropdown menu at the bottom of the page.
You can view all of the messages sent for a particular event in the same way; by clicking the 'Select an Action' dropdown menu at the bottom of the event's details page.