A.S.
I know that St. Benedict is a decently good Catholic school, which is very close to you (Irving Park and Leavitt). Here is their website: http://sbes.stbenedict.com/
Another very popular and good Catholic school in Lincoln Park is St. Clement. I know there is a long waitlist for that school.
Sacred Heart is another school I've heard good things about, located up near the Loyola campus: www.shschicago.org
There are several very good, very expensive, private schools in Chicago that are located more centrally or south in the city, but worth looking into:
Catherine Cook School
Francis Parker
Latin
University of Chicago Lab
Good luck in the search!