So an elastic IP is just an AWS provided IP that they hand over to you... it's free while your instance is running but if you stop your instance, you get a small bill (it's like $0.84 a month)
I don't have any elastic IPs. The only thing under EC2 is a security group that it won't let me delete, but seems like no resources. My bill this month is $2.88 /shrug
People forget to clean them up after shutting down the instance (probably kept in case you want to keep your IP)