My state says TN which is Tennessee but it's not an option when I pick choose state. What do I need to do? Is there a way to enter it manually somehow?

Tennessee does not have an income tax.  Therefore, there is no need to enter any Tennessee state withholdings anywhere in the tax return.  

You did not say specifically whether you are trying to file a Tennessee return or enter a form that has Tennessee listed in the state section of the form.  If you are entering a form, just skip that section of the form and do not enter anything.

I imported my W2 and TT keeps on telling me for box 15 "needs info" which is the state drop down unfortunately since Tennessee doesn't have state income tax there is no TN in the drop down.  How do I bypass and move on.  Help.

@mrug 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