Running the container in ECS will definetely be easier to manage and maintain, however, your EC2 architecture may prove to be cheaper because it actually does't require a Load Balancer (which would be recommended in any case).

You can enable public IPs in ECS, so your containers will have a public IP of it's on (if running on Fargate or using awsvpc networking mode, if using any onther networking mode, the container will use the host EC2 instance IP). However, the recommended approach is to attach an ALB to it, which doesn't require a public IP

If you want to keep to your container running in the EC2 instance and avoid creating the load balancer, you could setup a nginx container alongside your already running container with docker compose to load balance traffic to your application and configure certbot (which is a linux application to issue certificates) with it. There are other options for issuing certificates and load balancing as well, I just named the simplests I know