Ok Caleb, thank you for your help.
I installed the Hipay Wallet payment gateway for Woocommerce, so that I could have the credit card payment option available.
I’m having exactly the same problem. Everything seems to be ok. But the Shipping Address doesn’t appear on the checkout page, only in the My Account page.
I wanted a tab or something asking if the shipping address is the same as the billing address and if not I wanted it to be redirected to a page where they would define the shipping details.