If you are charged with the state law offense of driving on suspended license in Illinois, that is a class A misdemeanor criminal offense in Illinois. 625 ILCS 5/6-303(a). The maximum penalty for class A misdemeanor offense is up to a year in jail, up to 2 years probation/conditional discharge, and/or a fine of up to $2,500. 730 ILCS 5/5-4.5-55. Because this is a misdemeanor criminal offense, you’d end up with a criminal record that could cause you additional difficulties, like getting jobs, etc. I think you'd be wise to consult an attorney in IL who handles traffic matters. You may be able to get this reduced to some kind of infraction or at least avoid jail time.
You will, of course, also need to deal with the speeding ticket and any failure to appear charge that resulted from failing to go to court on that.
At a minimum, I expect you'll end up paying a lot in fines, court costs, etc., out of this.