When putting in my W-2, boxes 15-16 are filled out, but I live and work in TN so it's not listed in the drop down menu. I don't have state taxes. It won't let me continue

If your state has no state income tax, it is not in the drop down menu of Box 15 of form W-2. Just leave boxes 15-17 Blank, no spaces.

If you had no state taxes withheld because you live and work in Tennessee, leave boxes 15-17 blank. Then, you can continue with your return.