There is not an IRS website that shows you the status of a tax return when you have taxes owed.
However, you can go to the IRS tax account to see your payments and refunds - https://www.irs.gov/payments/online-account-for-individuals
You can also get a transcript from the IRS for the years you filed tax returns if the returns were received by the IRS - https://www.irs.gov/individuals/get-transcript
What did you pay? A tax due or the Turbo Tax fees?
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. And check your spam folder for them.
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?