If you need to connect to an Amazon RDS DBMS, you have to create a rule on the security group associated. If you dont have a fixed IP, you need to do this every time you want to connect to this DBMS.
The steps are:
- Go to AWS Console
- Log in with your AWS account
- Click on RDS
- Click on "Instances"
- Select the DBMS you need to connect, go to details and click on "Security Groups":

- This will open a new tab, click on Inbound and on Edit.
- Click on Add Rule, Select type: MYSQL/Aurora (If you have a MySQL instance) or MS SQL (if you have a SQL Server instance)
- On Source, put the IP where you need to connect (if its your computer, select My IP)
- Click Save.