I need a website to schedule my patients, and book online

I am seeking a skilled web developer to create a patient scheduling and online booking website, inspired by the functionality of docmein.com. The new site should feature a calendar interface for scheduling appointments, allowing patients to book online through customizable fields. A crucial requirement is the ability to limit the displayed appointment time options to a maximum of eight random slots, dynamically updating as bookings occur. Additionally, the system must restrict patients from canceling appointments online. Other essential features include seamless management of bookings and robust performance to eliminate glitches. If you can provide a solution that encompasses these functionalities, I would love to hear from you. I would appreciate if you would take time to visit and use the website docmein.com as an administrator before you take on this project. I am looking for something that is just as simple as this site. Thank you!