You could use the Parent fields on Account an Contacts to create a hierarchy. You would have to be a little careful as an Account can only have a parent of another Account while a Contact can have a parent of an Account or another Contact.
But from what you are describing it might be better to assign some sort of categorization to your Accounts (assuming your hospital record is an Account). Contacts would have a parent of an Account and the Account would be placed into a category for sorting.