Changing your schedule around implies that you went and rescheduled several meetings/appointments (presumably to squeeze another one in)
Changing your schedule could imply merely adding a new meeting, dropping a meeting, or adjusting some start/end times.
As an example, if you wanted to have a meeting from 3-4 tomorrow:
If I accept your meeting, no matter what else I do, my schedule has technically changed. If I have to bump other meetings to future dates, or cancel them, or significantly reorganize things to fit you in, I've "changed around" my schedule.
Consequently, "changing around" generally implies a greater sense of importance for this event/meeting than just changed.