To get the shipping options for current session.

 

<?php
    foreach ( WC()->cart->get_shipping_packages() as $package_id => $package ) {
         // Check if a shipping for the current package exist
         if ( WC()->session->__isset( 'shipping_for_package_'.$package_id ) ) {
         // Loop through shipping rates for the current package
             foreach ( WC()->session->get( 'shipping_for_package_'.$package_id )['rates'] as $shipping_rate_id => $shipping_rate ) {
                 $rate_id = $shipping_rate->get_id(); // same thing that $shipping_rate_id variable (combination of the shipping method and instance ID)
                 $method_id = $shipping_rate->get_method_id(); // The shipping method slug
                 $instance_id = $shipping_rate->get_instance_id(); // The instance ID
                 $label_name = $shipping_rate->get_label(); // The label name of the method
                 $cost = $shipping_rate->get_cost(); // The cost without tax
                 $tax_cost = $shipping_rate->get_shipping_tax(); // The tax cost
                 $taxes = $shipping_rate->get_taxes(); // The taxes details (array)
                 echo $label_name;
             }
         }
      }

?>