No, you wont have to add additional code. Both navigation views (desktop/mobile) are already there. But you will have to modify the classes which are loaded, so that your mobile navigation will always be shown, not depending on screen sizes. Right now your mobile navigation is just shown for specific screen sizes. When the screens are bigger, it immediately switches to your desktop navigation.
I’d love to be able to help you with this, but first I’d need to know if it’s a Shopify free theme you’re using or a third-party theme, as our support only extends as far as themes that we have developed ourselves! The more information you can provide me, the better I can help.