This is just to help anyone that gets caught out.
SQL Server Express does not, by default, run on port 1433 like SQL Server.
It can be set to run on a random port.
To find the port your instance is running on:
Open SQL Server Configuration Manager
Under protocols for SQL Express: "enable all"
In TCP/IP properties, go to the bottom of IP addresses, change or note the port.
Now open up AWS firewall for that port and you are ready to go :)