Can I delete the messages on my account after I read them ?

If you are talking about the submissions, yes, you can delete them.

1. Go to "My Forms" page and select the form with the submissions you want to view 

2. Click on "Submissions" button to view the form submissions page

3. The rest is quite intuitive as illustrated in the feature highlight illustration below: 

If you want to delete all the submissions at once, click on the Delete All Submissions button