Paying the fees does not file the return. Did you go all the way through the FILE section to click a big orange button that said "Transmit my returns now?" If you did not click the button to transmit the return, you did not e-file.
After you have e-filed you can watch for information in your email.
When you e-file your federal return you will receive two emails from TurboTax. The first one will say that your return was submitted. The second email will tell you if your federal return was accepted or rejected. If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.