These are two different things. A Cook County property tax refund is money the Treasurer sends back when you overpaid, when an appeal or Certificate of Error lowered a bill after you paid it, or when an exemption was applied late. The Illinois property tax credit is a credit on your state income tax return for property tax you paid on your principal residence.
Refund: how to check
Search the Treasurer's website by PIN or address, then use its "Overpayment Refund Status Search". The Treasurer refunds an overpayment without an application when its bank, card and property records show who paid; otherwise you file the online refund application with proof of payment (a cancelled check, card statement, or your lender's Form 1098). A reduction granted after you paid (an appeal, a Certificate of Error, a late exemption) has its own refund application; you have twenty years from the date the right to the refund arose. If your appeal succeeded after you paid the bill, expect the difference as a refund rather than a smaller next bill. See how a Certificate of Error works.
Credit: how it works
Claimed on Schedule ICR with your IL-1040: 5% of the property tax paid during the calendar year on your principal residence, not allowed above $250,000 adjusted gross income ($500,000 filing jointly). It is not a county program and cannot be checked on the Treasurer's site; the amount you need is your paid history (see payment history).
Refund vs future savings
An appeal filed this year lowers next year's bill. Only a reduction on a bill you have already paid produces a refund. Check where your township stands on the deadlines page.