To keep PostgreSQL databases in sync, you'll want a single master database that you write to, and one or more read-only slave databases that follow it using PostgreSQL's built-in replication. See the user manual. PostgreSQL does not support multi-master replication (where all replicas are writeable) natively.
In this case, though, I cannot imagine you needing a second database for load reasons. If you're on the EC2 free tier then you're using a severely throttled micro instance with woeful disk I/O performance on EBS. You'll get a thousand (or more) times more performance with an EBS-optimized large instance with a striped raid10 array of four EBS provisioned IOPS volumes. Even an ordinary medium instance is likely to perform massively better. I wrote a bit about this recently.
Trying to scale out at this point is totally unnecessary for performance. However, it's a good idea for data protection and redundancy. Consider using barman with hook scripts to store your base backups and WAL archives in S3, or adding a second PostgreSQL server in a different availability zone that runs a streaming replica of the master server. Remember to keep good backups off AWS too, like nightly database dumps.
