Generally, you pay taxes to the state where you live and to the state where you physically work (New York is a notable exception).
Since you live and work only in Tennessee, you would owe taxes to Tennessee (but Tennessee doesn't have an income tax, so you are safe).
However, as noted above, if you had taxes withheld by your employer for the state of Illinois, then you have to file a nonresident Illinois return to get your withholding back.
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