Is there a site that you can sell your own handmade product without an EAN number and without having a company?

Yes, You can even sell them at amazon if you have a seller account. However you need to get an approval for it which is not 100% gauranteed. whereas you can have EAN number at cheap price from https://codesforamazon.com/product-category/barcodes/ean-numbers/

which is reliable with 100% satisfaction gaurantee.