I don't owe any taxes this year, and am only due for a refund. I filed them before April 15th but did not have time to mail the physical documents to the IRS.

You posted that you filed before April 15.  If you e-filed your tax return there are no documents to mail.  All of your W-2 and Form 1099 tax data would be been included in the e-filed tax return.

Did you do this?

You complete your tax return by finishing all 3 Steps in the File section. In Step 3, to e-file your tax return, you must click on the large button labeled "

Transmit my returns now

What do you mean you filed before April 15 but did not mail?  If you actually efiled and submitted it you are done.  You don't need to mail anything.   When you efile you get back 2 emails. The first email only confirms the transmission. The second email says if the IRS (or state) Accepted or Rejected your efile.

When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. What does it say?

If you were suppose to mail your tax return you can try to switch to Efile
https://ttlc.intuit.com/community/e-file/help/how-do-i-change-from-mail-to-e-file-in-turbotax-online/00/26985 

If you are getting a refund there is no penalty for filing after April 15.  You can efile until Oct 15.