Hey, I am a web developer with 4 years of experience,
i can create a doctor appointment management system for you, as you described,
My approach to this project is like this,
For unregistered users (Guests)
It will show the home page, and find a doctor, book appointment now! They can do that but before doing that they will have to register and make a account, so basically it ll prompt them to make a account and then they can go onto finding doctors, booking appointment etc.
Or if you dont want them to register, their request will be shown to the doctor with a possible method of contacting them such as a Email address or so.
for the doctor's side, there will be doctor accounts, so if User A applies for Doctor B, doctor B will get a appointment request and then he can choose to approve it!
and then there will be a administrator's side, where he can Add/Remove and manage doctors! + he can see all the appointments and so because he's the administrator, (this is morely for owners and so)
I have described my approach to you, this is 100% changable! we can discuss further about this if you have any changes in mind or so. Please message me so we can get started!