Ok so I understand that you are in AWS and Docker already and Terraform is something you want to bring into picture for IaaC. and Yes, docker for production. Now, let's start with environment:
Assume you have three environments, Dev, Test and Prod. So you create three folders, Dev, Test and Prod which contain infra code for three environments. Now, I don't understand what you mean by infrastructure provided by docker but docker will contain your web servers and web application. Number of containers will depend on how large or small your application is and are you in micro services architecture. So what Terraform does for you is creating almost everything: Right from network structure(VPC, subnets, NACLs, gateways etc), autoscaling groups(I prefer this as you may want to use docker orchestration), security groups, IAM roles, policies to RDS and ECS etc.
So you can tag them in your code as per their environment and you create each of these components using Terraform modules.
So now you have Terraform code which creates infrastructure for you. Store your state file in S3 because you want consistency in your infrastructure state. Keep your database state file separate from other state files. You may want to have separate state files for your network, security groups, RDS, IAM, Cloudwatch etc.
Now comes the deployment part: Since you are in Docker, why don't you use AWS ECS? It will be easy deployment (Almost zero downtime) and orchestration will be managed by ECS itself. So now even deployment you can do using Terraform. Maintain a separate state file for this too.
You can create separate docker images for dev, test and production during your CI. If you do not have any docker tagging strategy, you may use $BUILD_NUMBER:$ENV for now. One of the purpose of using docker is that you don't need to care about where you want to run the container so identical docker images for Dev, Test and Production is almost always ok with some configuration changes.
You do not create anything locally. Use CI/CD tools such as combo of Jenkins and Git which triggers everything.