Is it possible to find which user created an account?
You have to create a custom module for this.


First you have to add a user field here admin/config/people/accounts/fields. Add a field that will check whether the user has been created by user with role "doctor". A boolean field would suffice. Mark the field as non-mandatory
Create a custom module. This module will provide an interface that only the users with role "doctor" can access. In the interface provide a button, clicking that button will create user with role "patient", also flag the field you created above.
Now in views create a page or block that will display the users, in the filter criteria of the view check whether the boolean field is flagged for that user.