Please refer to wp_script_is( $handle ) to check if a script is already enqueued or registered.
It’s a good idea to check before registering / loading a new script in WordPress. Since jQuery is included with WordPress and assuming you’re already using a custom WordPress theme I’m going to say it’s most likely already loaded.
You could check this by checking the “resources” tab on your browser (the Scripts folder) with your website opened.
Even simpler, you could check that jQuery is loaded on your website by going to the Console tab and typing in: jQuery(); – if that’ returns something, it means it’s already loaded.
I think, and correct me if I’m wrong, your problem is that you don’t actually know where to place your JS code for the autocomplete part. If that’s the case (your question was a bit ambiguous), please answer here so we can point you in the right direction.
Thanks.