Under state taxes, Box 15 is asking for my state. Tn is not available to select. I believe that's because we don't pay state taxes. Box is still wanting a selection.

Several  states do not have a state income tax.  So these states will not show up in certain drop down lists.   Leave boxes 15, 16, and 17 blank when you enter a W-2 for these states.

Alaska, Florida, Nevada, South Dakota, Tennessee, Texas, Washington and Wyoming

There's a glitch in TurboTax (TT). They're aware of it.

 In the meantime, you probably don't really need it.  If your employer put TN in box 15 of your W-2, it's irrelevant as TN doesn't not have an income tax. Just leave boxes 15-20 blank at the W-2 screen in TT.