Thanks for your message, I would be happy to take a closer look into this. Have you manipulated your coding in any way and if so, what were you trying to achieve when doing so? Are you able to share your store URL so I can take a closer look?
Thank you for providing me with a link to your shop, the site looks great! The changes you made via your coding are most likely causing the issue with your menu. I would recommend reverting the changes you made to see if that fixes the problem. That said, if you want to keep your search bar hidden, perhaps one of our friendly community members can offer you some advice. Shopify support is not able to support third-party coding customizations, however, if you are needing some quick help, you may also want to consider reaching out to a Shopify Expert.
I hope this helps you get on the right track for a solution, please do not hesitate to reach back out here with any questions about the above information.