PHP update password won't update

I am trying to update a users password when they enter their old through a HTML form. It won't work. I was wondering if there is a reason why my code isn't working. I was wondering if there is anything I can do to make sure the user can update their password.

       <?php

    session_start();


      if(isset($_SESSION["user"])){

      $email = $_SESSION["user"];

        include_once 'config.php';

     $result = "SELECT id, username, email, password FROM user 
        WHERE email='$email'";
 $result1=$conn->query($result);
 while($row = $result1->fetch_assoc()){
    $id = $row['id'];
    $email=$row['email'];
    $pass=$row['password'];
    $username=$row['username'];
    }


    if (password_verify($_POST['oldpw'], $pass)) {

    $newpw=$conn->real_escape_string($_POST['newpw']);

            $sql="UPDATE user SET password='$newpw' WHERE 
         username=$username and password=$pass";
        $result=$conn->query($sql);

            if($result>0)
            {
            $mysql="UPDATE user SET 
              password='$newpw' WHERE id='$id'";
        $result2=mysql_query($mysql);
            echo "Updated Successfully";
      }
            $updatepass="UPDATE user SET 
           password='".password_hash($_POST['newpw'], 
    PASSWORD_DEFAULT)."' WHERE id='$id'";
            $resultupdate=$conn->query($updatepass);

        $message="Your password has successfully been 
        updated";
        echo"Success";

   echo 'Password is valid!';
    } else {
  echo 'Invalid password.';
    }

    } else{

   header("location: login.php");

    }

?>