I'm not the greatest in JavaScript but I tested the code below and works. It basically uses the "describeLoadBalancers" API call to get a list of all your ELBs and then iterates through the result to look for your instance. If your instance is registered with a particular load balancer, it's name is output to the console:

// Require AWS SDK for Javascript
var AWS = require('aws-sdk');

// Set API Keys and Region
AWS.config.update({
    "accessKeyId": "<your access key>", 
    "secretAccessKey": "<your secret key>",
    "region": "us-west-1" // specify your region
});

// Get All Load Balancers
function GetLoadBalancers(fn)
{
    var elb = new AWS.ELB();
    elb.describeLoadBalancers(null,function(err, data) {
        fn(data)
    });
}

// Loop through response to check if ELB contains myInstanceId
var myInstanceId = "<your instance id>";
GetLoadBalancers(function(elbs){
    elbs.LoadBalancerDescriptions.forEach(function(elb){
      if(elb.Instances[0] != undefined){
        if (elb.Instances[0].InstanceId == myInstanceId){
            console.log(elb.LoadBalancerName);
        }
      }
    });
});

If anybody comes here looking for a pure bash solution.

Using jq to filter and parse the response of AWS CLI :

aws elb describe-load-balancers | jq -r '.LoadBalancerDescriptions[] | select(.Instances[].InstanceId == "<YOUR-INSTANCE-ID>") | .LoadBalancerName ' 

Also in aws-codedeploy-samples they define this function in common_functions.sh. I haven't tested it as I use ASG, but I suppose it will work

# Usage: get_elb_list <EC2 instance ID>
#
#   Finds all the ELBs that this instance is registered to. After execution, the variable
#   "INSTANCE_ELBS" will contain the list of load balancers for the given instance.
#
#   If the given instance ID isn't found registered to any ELBs, the function returns non-zero
get_elb_list() {
    local instance_id=$1

    local elb_list=""

    local all_balancers=$($AWS_CLI elb describe-load-balancers \
        --query LoadBalancerDescriptions[*].LoadBalancerName \
        --output text | sed -e $'s/\t/ /g')

    for elb in $all_balancers; do
        local instance_health
        instance_health=$(get_instance_health_elb $instance_id $elb)
        if [ $? == 0 ]; then
            elb_list="$elb_list $elb"
        fi
    done

    if [ -z "$elb_list" ]; then
        return 1
    else 
        msg "Got load balancer list of: $elb_list"
        INSTANCE_ELBS=$elb_list
        return 0
    fi
}

try this script:

#!/bin/bash

instanceId='i-XXXXXXXXXXXXX'

aws elb describe-load-balancers --query \
"LoadBalancerDescriptions[?Instances[?InstanceId=='${instanceId}']].LoadBalancerName"