PHP Classes, Using a Query function in another PHP file

I think you forgot to return you db connection link.

Database Class:

<?php
  class DATABASE
  {
    public function __construct() {
        $this->getConnected();
    }

    public function getConnected() {
        $dbHost = "localhost";
        $dbUser = "tysonmoyes";
        $dbPassword = "F!lmtrepid";
        $db = "tysonmoyes";

        $dbConn = new mysqli($dbHost, $dbUser, $dbPassword, $db);
        $this->dbConn = $dbConn;
        return $dbConn;
    }

    function queryDB($queryString) {
        return mysqli_query($this->getConnected(), $queryString);
    }

    public function close() {
        mysqli_close($this->connection);
    }
  }
?>

As mentioned in my comment and as others mention, return the connection foremost.

I personally think PDO would be a better option because parameterizing is really easy, but you are probably supposed to use mysqli_ so I would rework your set up a bit. This is not tested, just take notes of differences:

/classes/Database.php

<?php
class Database
    {
        private static  $singleton,
                        $con;
        # I LIKE TO RETURN THE SAME INSTANCE OF A CLASS HERE, OPTIONAL
        public function __construct()
            {
                if(!(self::$singleton instanceof Database))
                    self::$singleton = $this;

                return self::$singleton;
            }
        # I LIKE TO STORE THE CONNECTIONS AND RETURN IT INSTEAD OF POSSIBLY
        # CREATING A NEW INSTANCE
        public function getConnected()
            {
                # IF THIS STATIC IS NOT A CONNECTION, MAKE ONE
                if(!(self::$con instanceof MySQLi))
                    self::$con = new mysqli(DB_HOST, DB_USER, DB_PASS, DB_NAME);
                # RETURN THE CONNECTION
                return self::$con;
            }

        public function query($sql)
            {
                return mysqli_query(self::$con, $sql);
            }

        public function close()
            {
                mysqli_close(self::$con);
            }
    }

/config.php

<?php
# I PERSONALLY LIKE TO USE A CONFIG (PREFS FILE) TO STORE MY DB INFO INCASE IT CHANGES
define('DB_HOST',"localhost");
define('DB_USER',"tysonmoyes");
define('DB_PASS',"F!lmtrepid");
define('DB_NAME',"tysonmoyes");
define('DS',DIRECTORY_SEPARATOR);
# I ALSO LIKE TO STORE PATH CONSTANTS SO IT'S AN EASY AND CONSISTANT WAY TO
# LOCATE/INCLUDE FILES
define('ROOT_DIR',__DIR__);
define('CLASS_DIR',ROOT_DIR.DS.'classes');
# START SESSION
session_start();
# USING AN AUTOLOADER IS A MUST ON CLASSES
spl_autoload_register(function($class) {
    if(class_exists($class))
        return;
    # SHOULD RETURN A PATH LIKE:
    # /var/www/domain/httpdocs/myproject/classes/Database.php
    # WHEN CALLING $Database = new Database();
    $path = str_replace(DS.DS,DS,CLASS_DIR.DS.str_replace("\\",DS,$class)).'.php';
    # Presuming the file is named properly (and I have done the path right),
    # it would add the class file for you without using include anywhere.
    if(is_file($path))
        include_once($path);
});

/classes/User.php

<?php
class User
    {
        private $conn;
        # I WOULD SET ALL USER INFO TO AN ARRAY INSTEAD OF IN SEPARATE VARIABLES
        private $userData = array();

    # I MIGHT HINT AT TYPE HERE
    public function __construct(\Database $conn)
        {
            $this->conn = $conn;
        }

    public function createNewUser($username, $password)
        {
            $username = trim($username);
            $password =  trim($password);

            // Encrypt password
            $password = password_hash($password);

            // Check if username already exists
            # SQL INJECTION ISSUE HERE, YOU NEED TO BIND PARAMS HERE
            $checkSQL = "SELECT * FROM users WHERE username = '$username'";
            $checkResult = $this->conn->query($checkSQL);

            if($checkResult->num_rows > 0) {
                $error = "true";
                $errorMessage = "This username has already been taken. Please try again";
            }
            else {
                # INJECTION ISSUE HERE
                $insertSQL = "INSERT INTO users(username, password) VALUES('$username', '$password')";
                //$insertResult = $this->conn->query($insertSQL);

                // Get the user ID
                $userID = $this->conn->getConnected()->insert_id;

                // Set the SESSION globals
                $_SESSION['username'] = $username;
                $_SESSION['userID'] = $userID;
            }
        }

        public function login($username, $password)
            {
                # YOU SHOULD NOT BE INJECTING HERE. I USE PDO, SO I WON'T
                # ATTEMPT A GOOD FIX HERE...BUT A FIX IS REQUIRED
                # YOU SHOULD ALSO NOT MATCH PASSWORD HERE, JUST USERNAME
                # USE password_verify() TO MATCH HASH
                $sql = "SELECT * FROM users WHERE username = '$username'";
                $result = $this->conn->query($sql);
                $row = $this->conn->getConnected()->fetch_array($result, MYSQL_ASSOC);

                # DO A CHECK FIRST THAT THERE IS A ROW RETURNED FOR USERNAME (NOT SHOWN IN MY EXAMPLE...)
                # DO THE MATCH HERE
                $valid = password_verify($_POST['password'],$row['password']);

                if($valid) {
                    // Set Session Variables
                    $_SESSION['username'] = $username;
                    $_SESSION['userID'] = $row['userID'];

                     return true;
                }
            }

        public function isLoggedIn()
            {
                if(isset($_SESSION['username'])) {
                    return true;
                }
                else {
                    return false;
                }
            }

        public function redirect($url)
            {
                header("Location: $url");
                # YOU SHOULD EXIT HERE
                exit;
            }

        public function logout()
            {
                session_destroy();
                unset($_SESSION['username']);
                # YOU SHOULD PROBABLY REDIRECT HERE TO REFRESH THE SESSION
            }
    }

/index.php

# INCLUDE THE CONFIG ON ALL PAGES
include(__DIR__.DIRECTORY_SEPARATOR.'config.php');

$Database = new Database();
$User = new User($Database);