No, you still have a valid claim with your old insurance company even if you switch insurance companies before a prior claim has been paid. The insurance company has to honor the claim as long as the claim occurred during the policy period.
I agree with Neal! If you really want to be sure your rights are protected, you should hire an Illinois attorney who can help you through this.
Any answer given here is NOT legal advice and does not create an attorney-client relationship in Ohio, Kentucky, or any other jurisdiction. Answers provided are for general information only and should not be considered legal advice for any purpose. For legal advice, you should contact an attorney within the jurisdiction relevant to your issue.
It's the date of the accident that controls, so as long as your policy was in effect on that date you're fine. You have a right to have you're car repaired at a facility of your choosing. I'm not concerned about coverage, I'm worried your rental may be an issue due to the delay. If you're not in one now, then the delay will not hurt you. Otherwise, consider going to another shop or at least seeking advice from your insurance company about what to do. Get something in writing from them such as an email that they won't hold the delay against you (don't accept a phone call that could be denied later. Last, most policies limit rental to 30 days if you're going under your own policy. If you were going after an at-fault driver, then it would be for the reasonable length of the repairs without that limit. Good luck.