New to web development, suggestions on plug-ins for appointment scheduling

So as the title states I am quite new to web development. I've only been learning PHP, HTML, CSS, Javascript, MySQL for about a month now. All my previous experience is in Java. I have a project for my class where we have to create a web application for coordinating dentist appointments. Patients can log in, see a calendar and select an open time slot to sign up for an appointment. Dentists can also log-in to see their schedule and what patients have signed up for appointments, as well as the admin(receptionist, whoever they appoint to admin).

I've looked at quite a few plug-ins, but none of them quite match what I'm looking for, as you could drag and drop or put your "appointment" anywhere on the calendar. I need to be able to restrict that, and just simply have a time slot (1 hour for an appointment, let's say) for each room in the dentist office where a patient can sign up for the appointment. So does anyone have any suggestions or resources I can look at in order to accomplish something like this?