If you are going to move out of Illinois, your two DUIs are likely to follow you. Forty plus states are part of the Driver's License Compact (DLC) that means licensing authorities of the member states share driver license information.
Beyond the DLC there is also the Problem Driver Pointer System (PDPS) that searches the National Driver Register (NDR), a central database of information on drivers who have had their licenses revoked or suspended or have been convicted of serious traffic violations such as driving while impaired by alcohol or drugs.All 50 states and DC participate in the NDR.
So the state in which you move to will typically check the NDR or PDPS. The PDPS points the inquiring licensing bureau to the State of Record, where an individual's driver status and history information is stored. This helps with the basic tenet of each driver nationwide having only one driver license and one record.
Your former DUIs and current revocation of your license in Illinois should thus be seen by whatever state you choose to move to. There might be states that are willing to give you a restricted license or allow you to drive with a permit if you have an interlock ignition system. To find out of what states might allow this you should contact the Department of Motor Vehicles of the state(s) in which you are interesting in moving to.