I just switched 3 kids from a Catholic school to the public one. I am not in Chicago and it has been a VERY positive experience. In my situation, our schools are excellent and the Catholic schools were starting to fill the classrooms with 32-35 kids (no aid).
I have actually run into problems with my 9th grader missing some basic algebra skills! My advice with your ninth grader would be to call the high school office and find out who your counselor would be and meet with him/her. They will help you figure out the classes he should be in. I thought that since my son went to the Catholic school he should be in an advanced math class, but sadly we found out how badly the math lacked in the Catholic school. I was an involved parent and they made a big deal saying how they finished the book, but apparently it wasn't in a way that my child remembered!
Anytime you change will be hard. Even with my 7th grader we met with the counselor and talked about how that child would meet people, even to sit with at lunchtime. Have you boys done any sports with kids in your area? I found out that helped because then they say some familiar spaces.
I wouldn't worry too much about switching right now. They has been lots of review time and it seems like just the past 2 weeks have been heavy with the homework. I don't think it will be that hard to catch up.
You can send me a private message with any questions.
M.