Once you've landed a job as a school librarian, whether at a private or a public school, there is a certain amount of "culture shock" you are likely to experience. In your career as a public librarian, it really was all about you - you were working in a library, surrounded by other librarians and library paraprofessionals, and everyone who walked in that door was in need of some sort of library services (with the possible exception of those just in need of a bathroom). Once you are in a school setting, though, chances are you're working solo- or, at most, with just one or two other library colleagues. For the most part, your coworkers will be teachers, and if you are lucky, you will come to be regarded (by colleagues and students) as a kind of a teacher, too. If you are unlucky...well, prepare to feel rather lonely. A school, unlike a public library, is a very small and insular community - you will be seeing the same faces (adults and children) every day, so the sooner you can establish a basis on which to relate to them, the better.
Another shock to the system comes if you find yourself in a position where you will be expected to serve as a "teacher librarian" - instead of just taking things as they come, answering patron requests on an as-needed basis as you do in the public library, you may now be expected to teach regular weekly classes to anywhere from 15 to 25 classes (maybe more) consisting of from 15 to 30 students each (and sometimes quite a few more). Lesson planning can be quite a challenge, especially if you are new to it, and your best bet is to ask for help from the experienced teachers as well as to get some idea from your principal or division head as to just what types of lessons or activities they would like you to present at each grade level.
Perhaps the most difficult hurdle to overcome can be that of student discipline. In the public library, children come singly or in small groups, and are supposed to be accompanied by parents if under the age of 12 (although this is not always the case). With young adult patrons, if they become rowdy you always have the option to eject them from the library, and may even have a security guard to help you enforce this. In a school however, you are expected to cope with managing large groups of children on your own , on a daily basis, and any failure to keep them under control may reflect badly on you. Again, your best recourse in dealing with the discipline problem is to enlist the aid of classroom teachers, both in giving you "heads-up" warnings about the more difficult pupils and in sharing the strategies they may have developed in the classroom.