This is tough. You must certify for unemployment every week. Here’s the section of the Illinois unemployment handbook that deals with your issue:
If you had earnings since you last certified. Report the gross wages for any work performed, full or
part-time. Gross means before taxes or other deductions, not your take-home pay. Earnings in the
form of lodging, meals, merchandise or in any other form should be included.
Remember, wages must be reported for the week when you earned them, not when you actually received
them. If your gross wages earned in any week are less than your weekly benefit amount, you still may be
eligible to receive a full or partial benefit payment.
So a lot depends on how much you earned being an Uber driver. Now that the $600/week federal assistance has ended (and no idea when/if Illnois will pay out the extra $400/week) it might be better to drive an Uber than get your traditional unemployment benefits. Or maybe you will still get “some” unemployment benefits even after reporting your Uber income — depending on the amount you earn.