Yes, be sure to select nonresident for both IL and MA.
NY should work fine as long as you are prepared to enter the necessary information in the NY return. I believe that NY does bring you to the Other Tax Credit section and allows you to edit the entry. You may not need to but you should have the income (from the W-2s) for each state and the tax liability (from each state's return) and you will be prepared.
@sg11sg
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