Of course. That doesn't mean that you can't go to court to have the amount of support that you pay reduced due to your current situation. You obligation to feed and clothe your child continues until they are an adult. You need to meet with an attorney in your area to discuss your options. Good luck to you!
I assume that you are currently ordered to pay child support and that such order was entered based upon a previous work history. You are required to comply with the order regardless of any personal situation you are in until there is a new order either reducing, abating or terminating your obligation to pay current support.
When you filed for unemployment you should have informed the office that you have a child support order and in turn you would be awarded an additional dependent allotment from the government. This amount would likely be the amount set as your new current support amount once you file with the court an petition to modify child support pursuant to state law 750 ILCS 5/510. If you do not file the petition and ask the court to modify the amount you are required to pay the amount as order, not the dependent allotment amount the government will give you.