I am being charged even though I have reserved instance

Hello.
How many Reserved Instances were purchased for which option?
If you purchased with "No Upfront" or "Partial Upfront", you will see a charge on your monthly bill.
https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_WorkingWithReservedDBInstances.html

In addition, if you have purchased only one Reserved Instance and are launching an RDS with multi-AZ enabled, you will be charged for multi-AZ.

Reserved Instances are applying on an hourly basis. So, if you are constantly running your db instances, then the RI discount will apply each hour if the attributes of RI match the attributes of your running instance.

But note that the RIs do not apply retrospectively. Let's say, you bought your RI on the 28th August at 10:00 in the morning. If all attributes of your running db instance and your RI match, then you should start seeing the discount applying from the top of the hour (10:00 after you purchased it). Any hours in this month prior to your purchase are not covered by the discount, and are still charged on-demand (were charged on-demand before your RI purchase).

Note that if you are looking in the billing console - it usually has around 8h delay (it's not updated real-time), so it's better to look for the charges for your RI the next day. As soon as the RI discount starts applying, you will see a different line item in your bill, that will look something like "covered by reserved instance" and then number of hours and $0 cost, and this will mean that the resources are being covered by RI discount.

In addition to my previous response - of course, make sure that you purchased your RI in the correct region, in the same region where your db instances are actually running (this is a very common mistake that customers make when they accidentally buy RI with wrong attributes). And as stated in another reply, if your db is running multi-AZ, but you purchased single-AZ RI, it means that only half of your db will be covered by RI discount at any single hour. You'd have to purchase another same RI to cover another half.