If you want to allow a remote user to browser your local shop, you need to make sure that the sales channel domain of your Shopware match the static hostname you are using.
Why? Simply because links on the shop are being rendered through TWIG by using the configured sales channel domain and not the domain being currently used.
If you don't pay attention, you might see the first page working, but as soon as you click somewhere it would redirect to the local development host (or localhost), which does obviously not work from remote.
You can either adjust the domains manually, or use this automation option.