Hi,
I am an IoT consultant and AWS certified solution architect. I have worked on several IoT based projects for industrial clients in last 4 years.
As per my understanding of the project, if you are using AWS IoT core, you dont need to set up MQTT server as IoT core comes with an inbuilt MQTT server. However, IoT core needs to be configured as per your requirement. Data from MQTT can be parsed and stored in SQL database like AWS RDS. or you can also use AWS DynamoDb for serverless design.
Feel free to get in touch with me for details. I m based out of Bangalore and make frequent visit to Chennai.