Here is my two cents on the topic, the question is not really related to ecs, it applies to any body deploying their apps on docker.
I would suggest separating the containers, one for nginx and one for API.
if they need to be co-located on the same instance, on ECS you can define them as part of the same task and on kubernetes you can make them part of same pod.
Define a docker link between the nginx and the api container. This will allow the nginx process to talk to api container without the api container exposing its ports to the host.
One advantage of using the container running platforms such as kubernetes and ecs is that they ensure each of the container run all the time and dynamically restart if one of the processes/containers go down.
Separating the containers will allow these platforms to monitor both the processes separately. When you combine the two into one container the docker container can only run with one of the processes in foreground, so you will loose the advantage of auto-healing for one of the processes.
Also moving from nginx to ELB is not a straightforward solution, you may have redirections and other things configured on the nginx, which are not available on ELB(As of date).
If you also need the ELB, there is no harm in forwarding the requests from the ELB to the nginx port.