How is RDS for SQL Server Express charged?

From the docs

AWS Free Tier with Amazon RDS

• 750 hours of Amazon RDS Single-AZ db.t2.micro Instance usage running MySQL, MariaDB, PostgreSQL, Oracle BYOL or SQL Server (running SQL Server Express Edition) – enough hours to run a DB Instance continuously each month
• 20 GB of General Purpose (SSD) DB Storage**
• 20 GB of backup storage for your automated database backups and any user-initiated DB Snapshots**

** Backup storage is free up to 20 GB or the size of your DB storage, whichever is less, and requires you to have at least one DB instance running in your account. If you exceed these limits, or if you terminate all DB instances in your account, backup storage will be charged at standard RDS rates.

For your case ensure you are running a single-az db.t2.micro with no more than 20GB of DB storage. To verify if you are falling within the free offering refer to the billing console and look at your bill. From here you will be able to see if you are being charged and if you are you can determine what you have launched outside the scope of the free offering.