http://www.chicagoelections.com/en/your-voter-information.html
That site always has worked well for me.
If you received a voter registration card a few months ago, you're registered. Perhaps if you used the Illinois rather than Chicago site (above) your new information had not been properly entered. I frankly wouldn't trust the state site.
You should (a) call the Chicago Board of Elections to verify; and/or (b) call your alderman's office. Your alderman should also be able to give you a list of the closest early voting sites in your area. Or you can check it here--the full list of early voting sites is provided by the Chicago Board of Election Commissioners. You may use ANY early voting site in the city. It does not have to be in your district. Show them your card. You should be good to go:
http://www.chicagoelections.com/en/early-voting.html
PS: THe card you were sent should have your federal and state districts as well as Cook County and judicial districts (it's a lot of different numbers). At the Chicago Bd of Elections site, you can also download a sample ballot that reflects the races in each of your districts--that is, if it has your registration verified.