If your return was rejected and you have fixed and resubmitted your return, you can check your e-file status here to ensure it went through. Your return would most likely say "Pending" unless it moved through the system quickly.
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.