As your application does not seem to support clustering with session management to share sessions across the cluster I would recommend you to configure session stickiness for your load-balancer. This will bind a user's session to a specific instance. Then, all user's requests will be processed by that instance only.
You have two choices there. Your application supports sessions so you can tell your load-balancer directly what application cookie to use to track the instance for each user's request.
Otherwise you can enable so-called duration based session stickiness when load-balancer itself is inserting a specific session cookie to the responses to bind subsequent requests from the user to the same instance.
Following screen-shots are self-explanatory. You can configure session stickiness from AWS web console -> your load-balancer description tab -> edit port configuration
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More details can be found at this page.