You'll have to determine the portion of your income that was earned within New York. Then file a non-resident NY return in addition to your home state IL return. You'' be able to take a credit on your IL return for the taxes paid to NY, so you won't be double-taxed.
See this FAQ for the process to follow in TurboTax: https://ttlc.intuit.com/questions/1901271-how-do-i-file-a-nonresident-state-return
**Answers are correct to the best of my ability but do not constitute tax or legal advice.