Do not contact admissions directly. Since you are in state, admissions is surely familiar with your high school and will be much more likely to take a call from your guidance counselor. Ask your GC to make a polite inquiry on the basis of determining whether an appeal request would be worth the effort. Of course there is not much effort in filing an appeal, but this will give admissions an opening to share an explanation for the rejection if they are inclined to do so. I would not expect much but this is your best chance.
IL residents receive well under half of offers in CS in ENG. The average ACT score for an accepted applicant was over 34.5 last year, and that includes underrepresented demographics. This year applications went up 25%+.
Applications are up 60%+ in just the past two years. Last year most (two thirds) of perfect ACT scorers received no merit scholarship from the College of Engineering. Just a couple of data points. You are surely qualified, but not over qualified.
Illinois does not practice yield management/protection. In fact they don’t seem to care much about their selectivity at all (not even on common app and they bend over backwards to offer 2nd choice and DGS which kills their selectivity measurables). They accepted hundreds of 34/35/36s this year.