non-Webflow domain search is not working.
https://vinnys-fabulous-site.webflow.io/ (search is working here)
https://www.h-choice.co.uk/ (not here)
Here is my public share link: LINK
(how to access public share link)
Your site has some programming issues,
the main one is that you are using jquery in your <head> area, before the jquery library is loaded.
Move that to </body> custom code area, and wrap it so that it executed when jquery is ready.
https://learn.jquery.com/using-jquery-core/document-ready/