Is it legal for government housing to charge me rent if my only income is my 4 year old autistic son's disability check?

First, the money is your son's ... it is not your "income."  If the funds are used to benefit him, that is to provide him housing, I don't think this is a problem.  I do not believe that it is illegal if the rent is greater than his benefit check. Because you live in Illinois, you will want to speak to a local attorney.  Click the picture of the house above (next  to "Find a Lawyer") to find an attorney that can help.  Your type of law is "Residential Real Estate.