Turbo Tax showed no errors and the IRS rejected my return. I filed Head of Household because Turbo Tax identified that as my filing status. However, the IRS rejected it

Turbotax is not responsible if you provide incorrect information.  

Are you saying the IRS rejected your attempt to e-file?  That means that some piece of information they have on file is different than what you provided, and they can't accept your return for automatic processing.  What exactly is the rejection message?  It may have nothing to do with your HOH status.  If you believe your return is correct, you can print and mail it.  If you already paid, you do not have to pay again to print your return and mail it in.

Or, are you saying the IRS accepted and processed your return and has now sent a letter disputing something in your return?  That is a completely different problem.  What are they disputing?