Hi, there!!
I'm a public librarian (I work in adult services), but I will tell you my experiences and experiences of my friends who are children's librarians
First, I'm pretty sure that if you want to be a school librarian in the public school system, you also have to have a teaching degree. Private schools (like Catholic schools, etc are perhaps a different story. I have a friend who only has her MLS and is a school librarian, but she's at a private school, and another friend (also at a private school) who has her teaching degree but no MLS and is school librarian. So, it depends on what type of school you want to work in. Actually in Illinois, you don't even need your MLS, but an endorsement added on to your teaching degree. (But when I was in library school, there were many getting the full MLS because it's only a few credits more to get the Master's degree rather than just an "endorsement") So you might want to look into that if you're interested in working as a school librarian.
As far as public librarianship, all you need is your MLS. Of course, with being a school librarian, there are advantages over public librarianship - one being salary. School librarians make much more than public librarians (unless you work in a private/Catholic school). School librarians also work on a school year schedule, having summers off. Public librarians work year round, and if you're a Children's librarian, summer is the busiest time because of summer reading programs.
The Children's librarians here at my library are excellent. Each specialize in something different. Pre-school, school liasons, storytellers, etc. They're awesome!
Now as far as library school goes. Any background will do. It's interesting to see what librarian's bachelor degrees are in! Many are teachers, but I've seen former lawyers, science majors, all kinds. There aren't that many schools that have MLS programs. Many just go to what's closest to them, or they do it online, which seems to be the growing trend. There's a library school in the Chicago area but everyone I know who's currently in school does it online through the University of Wisconsin at Milwaukee. The major advantage - they offer in-state tuition and it makes it cheaper than the school that's in the Chicago area (it's a Catholic university and expensive!).
My advice would be to try to get your "feet wet" and see about working part time in a library while you're in school. I don't know if you plan on going to school full time or not, but it seems to make all the difference. I worked in libraries prior to going to school and it was so helpful to be in the field already, especially for having access to resources for your homework (especially if you're doing your MLS online) You can work in a public library or college library - anything. It's something to put on your resume and will give you a jumpstart when looking for a job in the future (it's true!! Something they don't tell you about in library school!! At least not mine).
The American Library Association website has useful info - they offer many scholarships, too!
www.ala.org
I hope this wasn't too long - just wanted to give you my input!
By the way, with your background, you could also work in a special library - like a studio/film/tv station, etc. They do exist! If you have any more questions, please don't hesitate to ask! You can PM me if you'd like, too!
Best wishes,
Carmen