Medicare is a program you pay into for your future health insurance after you retire (over 65) or become permanently & totally disabled, if you paid into it long enough to qualify.
If you had any health insurance through your prior employer, it ended when you quit. Your company would provide info on paying for COBRA to continue coverage while unemployed, if you qualified for that. If you did not get an insurance card while employed, you had no insurance. If you did not get COBRA info on departure, you do not qualify for that.
Check your paystubs. If you got health insurance through a group plan with your employer, your insurance premiums would have been deducted from your pay, and that deduction noted on your paystub.