Hello there,
May i know what is your DBMS installed/used in your AWS? a SQL DBMS like Mysql and MSSQL or a NoSQL DBMS like MongoDB?
I myself runs my server at AWS,
i also able to manage Environment that runs on the top of Ms Azure .
But one think so far i know that AWS allocates a dedicatep IP address for you(elastic),
even if its not Dedicated, i can still manage your database to be pointed correctly with Dynamic DNS service.
Regards