Advice on Developing a Desktop Application

Question

I am building a healthcare application that will manage sensitive patient health information.  I could really use some guidance on how to proceed.  Thanks in advanced for all of your suggestions!!

My requirements:

1.) I prefer building a Desktop Application using .NET Core.

2.) I prefer using Microsoft SQL server for the back end.

My customer will be a number of different hospital systems.  I don't work for these hospital systems.  Is there a way that I can build an application which allows these hospital systems to install my software on hospital desktop computers but use the hospital system's 1.) domain accounts to login, and 2.) use the hospital system's own SQL server to store patient data.  I presume this will create some form of trust issue because if the physician logs into my application using their hospital credentials I can technically steal their credentials.

We can assume that the hospital system can allow domain account access to the SQL server and that I will create a deployment script that will create the database needed on the SQL database.