Call (844) 598-9841 to make a payment using our automated phone service. This service is available 24 hours a day, 7 days a week.The County offers two medical benefit plans: Blue Advantage HMO and Blue Cross Blue Shield PPO. Please see plan details below. To apply for Medicaid, Illinois residents can visit the Application for Benefits Eligibility website to start the health care coverage application. INSTRUCTIONS: Complete and sign this form. Make a copy for your records. CountyCare's Medicaid health plan offers access to 70 hospitals, benefits like LASIK and dental plus rewards that promote a healthy lifestyle. CareLink is a free program that helps Cook County residents cover the cost of care at any Cook County Health facility.