How to access different MySQL databases in a same instance in Amazon RDS?
Well, I was living in a lie.

The simple reason why I couldn't access my table on RDS was because RDS runs on Linux and MySQL table names are case-sensitive on Linux, while my local DB runs on Windows where MySQL table names are not case-sensitive.

About multiple databases in a single RDS instance: RDS does accept multiple databases. It's just that, for an unknown reason, only the initial database of the instance is always displayed in the dashboard. This still doesn't make sense to me because this database has nothing more than other ones, apart being the first one.