Paul, If Shiny Server is installed on the AWS instance, it will be running on port 3838 by default. The port is configurable, but you should be access your applications at a fixed port. Your application must be in a directory that is known to Shiny Server. By default this is /srv/shiny-server directory. But it is also configurable. Please refer to the Admin Guide for more information:
Setting up a predictable path for execution of a shiny app on AWS
I seem to have lost this post: The IDE keeps assigning new paths within the URL for the App. How do I fix the URL execution path. Is there something I'm missing. I'm using the shiny server AMI on AWS.