There are many different types of medical mobile apps, for example apps for clinical use, for remote monitoring, reminder apps, apps for maintaining a healthy lifestyle and other. If you want to start I recommend to read this blog steelkiwi.com to know main features of successful medical mobile apps. Price of such app will depend on the complexity and the amount of hours spent on its creation.
Good question. I think it depends on what the purpose of the app is - learning more about your health, getting a prescription, talking to your doctor, or managing everything?
I ask because my brother is an app developer for a large health insurance startup. We've had many conversations about design/function/purpose.