If you live in one state and work in another, the state where you worked will expect you to file a "Non-resident" tax return and pay tax on the money you earned there.  Your state of residence will tax you on your world-wide income and give you a credit for taxes paid elsewhere.

You should complete your non-resident state return before you do your resident state return so that the credit flows correctly to your resident state return.

The state that the company is in does not have state income tax. They held out taxes for the state I live in.

States don't care where the company is headquartered they care about where the work was done.  You need to file an IL Non-resident tax return, report and pay tax on the income you earned in IL.