Tasks, reminders and the clinic calendar.
Tasks with a date and a person, reminders set on the day you mean to do the thing, and a calendar of the days the clinic is open or closed, with the holidays suggested.

Tasks
What it does.
Today, mine, all, done
Four views, and a box to add a task.
Reminders on the day
Put a reminder on the day you mean to do the thing.
Open and closed days
The weekly hours, closures and holidays in one calendar.
A person on each task
Who it is for, and who set it.