You are correct that the Illinois Department of Financial and Professional Regulation (the state agency that issues property and casualty insurance licenses) will examine your criminal history as a part of their standard background investigation. They do this investigation for all applicants for licenses, not just insurance licenses.
The best thing to do is to contact the Department by phone at (217) 785-0800 or on their website at http://www.idfpr.com/. You can explain your specific situation and they can advise you from there.
If you need to seek a pardon from the governor, you must draft and submit what is called a "clemency petition." It is designed to be done yourself without the help of a lawyer. You can find forms, information, and instructions regarding Illinois clemecy petitions at the Prisoner Review Board's Website at http://www.state.il.us/prb/prbexclemex.htm.
NOTE: This answer is not intended to be legal advice and should not be construed in that way. This answer does not create an attorney-client relationship and no such relationship may be created absent a signed retainer agreement. The author is licensed in Illinois only, and his answer is for educational purposes alone.