I installed TTax Deluxe but ended up having someone else prepare my taxes. Is there some way I can still efile using TT, even though it isn't the TT file?

Why didn't the person who prepared your taxes efile them for you? If they were already printed and mailed instead of being efiled, the IRS requests that you do not efile a return after already mailing a return. 

If they were prepared using the TurboTax program, you should be able to move the .tax file from the computer of the person who prepared the return to the TurboTax program on your computer.

You need to have the file ending in .tax2019 to file using Turbo Tax.  If you already had the program they should have used it to prepare your return.  What did they use?  Did you pay them?  Turbo Tax is not licensed for tax preparers.  If they prepared it they should file it or give you printouts to mail.  Maybe you can get a refund for the program.