You need a court order
If you have a court order, but your ex stopped paying child support at some point, or never paid at all, you have a good chance of collecting any past-due amount. You will probably have to go to court to enforce the order. There generally is no deadline.
The parent, not the child, is the one to collect
Adult children often wonder if they can collect past child support from a parent who didn't support them growing up. The custodial parent is the one who needs to petition the court, not the child.
Verbal agreements probably not enforceable
If you and your ex had a verbal agreement about child support, or even if you wrote one down on your own, you'll have trouble collecting any amount that wasn't paid as agreed. You need to get into court and get a formal order for child support in order to enforce it later.
Support beyond age 18
In Illinois, child support may extend beyond when the child is a minor. If the child is still in high school at age 18, support can continue. If the child is going to college, child support can be set up for school tuition and related expenses. Again, you need to have a court order. It's up to the judge whether support will be awarded for college. Generally speaking, the judge will consider the financial status of each parent as well as the education plan of the child.