Allison,
What Student Information Management System do you use? Most of these providers have an internal area where you can add notes to a student's account and that would allow each department to know if another department needs to speak with a specific student. If not, does your school offer any computer programming courses? If so, there may be an instructor or a student that could write you a program that allows this type of student tracking.
I definitely see this as a concern that would require a method to manage to ensure that students are getting the best service.
Sincerely,
Chyrl Ayers