Legal Question in Employment Law in Illinois

I don't know why you are concerned with whether or not this is a "proper write up." In Illinois, your employer does not need a reason to terminate you nor does the employer need to give you any type of notice unless they have made a practice of formally doing so and/or they outline such a process in their employee policies. Your big concern right now should NOT be whether or not this is "formal." You are on notice that your employer is not happy with your performance. That should be your big concern. Put your energy into fixing that problem rather than creating additional ones.