Single versus Multiple databases
Designing a platform: one database or multiple databases? is relevant background reading for your question.

You're possibly approaching this from the wrong angle. Is there really going to be a single, all mighty, all encompassing, one true system called "THE Hospital Management System"? Or will there be:


Appointments Management System
Patient Records Systems
Medicines/pharmacology database (highly likely to be something bought in, rather than re-invented)
... ?


I'm sure there are dozens of other applications to add the list. Each of these is a separate application and probably a separate database, all of which need to talk to each other via a defined interface. One big application with one big database is a fast road to chaos.