> when I test the zipped folder on my computer...
Some Operating Systems (like recent versions of Windows) allow you to view the contents of a ZIP file by selecting it in the File Explorer application (like you would with a normal folder), however while you are able to run a HTML file seen in such a view unfortunately that HTML file will not be able to access any Relative referenced extenal media.
You will need to extract the contents of the ZIP file onto your local hard-drive if you want to test the contents of that ZIP file, once you have done this the extracted HTML file should be able to access the extracted media files.
> When I upload it to itch.io, it says that it cannot find index.html
I don't have an Itch.io account but after reading the information found here I wondered about the naming of your files and folders.
Most Operating System (excluding Windows) are letter case-sensitive when it comes to the names of files & folders, especially when used within an URL, so it is common for developers to only use lower-case letters when naming files & folders. Space characters in such names can also cause issues which is why they are generally replaces with either an underscore character or a standard dash (minus sign), and generally all other Punctuation (excluding the full-stop / period) characters are removed.
If the name of your index.html file isn't in all lower-case characters then Itch.io may not be able to find it after they extract the files from your ZIP file, the same could be true for the name of the ZIP file itself or any of the media files contained within it.
The page I linked to also contains information about ZIP file requirements, make sure your ZIP file meets them.