MYSQL RDS on EC2 instance

Assuming that EC2 and RDS are in the same VPC, check the security group associated with the RDS instance has an inbound rule allowing TCP port 3306 from the EC2's IP address, and that the security group associated with the EC2 allows TCP port 3306 outbound to the RDS instance.

If they're in different VPCs then check the VPC peering setup, and the route tables for both subnets.