Hi shearg,
I see a James G Cook, age 28, in Chicago's Ward 25, born in England, Immigration appears to be about 1884 (years in US looks like 16). Not living with a Dolores though. Has a wife, Eleanor, age about mid 30's (difficult to read), born in England, daughter Florence, age 2, born in Illinois.
I'm not finding a Dolores/Delores Sherwood in Illinois either. I see a Mrs. Sherwood b. abt 1862 Germany, in Proviso, Cook, Illinois. If this sounds like her let me know and I'll look more into her.
Laura