Appointment Book for Patients

I am in need of a web-based appointment book for medical appointments. It should have the ability to allow patients to select a free appointment slot from a list of doctors. The patient will need to pay online once a time slot is finalised and after basic patient details are provided.

We have a prototype solution already but need to improve the overall design and look & feel of the UI. Design needs to be responsive and support both a regular desktop/laptop/tablet screen and smartphones.

Thank you for taking the time to consider my project.