Firstly, get_shipping_method is a function. You seem to be using it as a variable.
Secondly $order->get_shipping_method() returns Shipping method label, which you’re trying to compare with id.
Now you can either compare Titles, or use
$order->get_items( 'shipping' );
which returns an array with name, type, method_id, cost and taxes, and use method_id for comparison.