You don't need to file at all in Illinois. The only reason you would need to file in Illinois when your only income is reciprocal W-2 wages, is if your employer withheld tax to that state and you needed a refund.
You will file just a Wisconsin return and report your wages as if you had earned them there.
If you accidentally bought 2 states, here is how to get a refund: How do I request a refund for my TurboTax product?
Here is more information on reciprocal states: What is a state reciprocal agreement?
