R.L.
How high was your child's level? 10? 50? Is the doctor recommending medical treatment, including hospitalization, or just identifying and eliminating the source of the lead and then restesting?
Sometimes flaking paint can leave dust on toys that the child injests, so it may not be that actual paint chips are evident and being eaten. If you rent, the landlord is responsible for addressing the problem. If you live in the city, you can call the City of Chicago and they will send an inspector who will test for lead and tell the landlord, or you if you own, what has to be done. I suspect the suburbs must have similar requirements. If you have a situation where the landlord was aware of the problem and did nothing, then you do need a lawyer.