Hi there,
As I have understood,
You want a web application built from scratch, which will hold all of the mentioned functionality. But it will not be on wordpress or anything similar template based.
I have few suggestions for you, when you don’t want to o with wordpress, then why don’t you move to more secure, and more flaxible Asp.Net MVC.
This way, you can have it changed anytime you want, more flexibility to implement post deployment changes, solid architecture, and hack proof design.
And most importantly it will be light weight, I will make you this application on Angular and MVC.
I have a good design as per architectural view of your project, starting from doctor to patients, all things can be done in proper way, with Unit Testing as well, so that next time anything required, it will not get broke.
I am having 8 years of experience designing web application.
Having lots of things to discuss.
Weather you award me this project or not, I wanna help you with some suggestion which will help you get a strong product.