There is an option to increase this max DB connection value by creating a DB parameter group for this Micro instance.
Does it affect if we increase max connections in AWS RDS for MySQL
In this blog, we explain you with an example how Does it affect if we increase max connections in AWS RDS for MySQL. AWS RDS t2-micro running MySQL 5.5 most of the time it gives “too many connections” error. As per the DB instance type t2-micro it allows 66 maximum connections concurrently.
Changing the number of connections increases the amount of memory each connection can demand to this : (+ + + ) X
Amazon has to set the number of connections based on each model’s right to demand a certain amount of memory and connections.