If you use a load balanced environment, your domain should be pointing
to the load balancer, so i assume you are on a single instance environment.
In this case, you can use .config files and aws cli to automate the DNS
record change (see http://docs.aws.amazon.com/elasticbeanstalk/latest/dg/customize-containers-ec2.html).
Another alternative would be to launch the environment in a VPC and attach
an ENI with a fixed IP to the instance, that could avoid DNS caching
But considering the ELB costs, i would not go that far, just launch a
load balanced environment with a single instance and register that ELB in
DNS (an ALIAS record, if you are using Route53).