Helpin aunt find her deceased husbands birth parents for medical history

I am helping my aunt (who has no computer and no idea how to begin a search) look for her deceased husband's birth parents for any medical information that would be helpful for her children and grandchildren. Her husband was adopted in the 1930s (maybe 1934-36) from the St Geneieve Church in Chicago Il. The adoptive parents were Edwin and Catherine Steinmetz and resided in Chicago. The child was named Edwin G Steinmetz. Edwin is dead as are his adoptive parents. Unfortunately, the entire family never talked about Edwin being adopted (just hushed whispers) so not much information is known about the birth mother or father or even the adoption process. The little bit my aunt remembers her mother-in-law saying is that the mother was from an influential family in Chicago, who had been away at college (out East?) when she got pregnant. In fact my aunt remembers Edwin's mother saying she actually saw the birth mother several times in Chicago when Edwin was little (no contact was made). Any help on how to proceed in finding medical history of Edwin G Steinmetz birth parents would be greatly appreciated. Thank you.