You can still use Bitly, but have the bitly point to your own site first, then redirect to your affiliate link from there. With a bit of work you can do the same with any post you make to Pinterest, so that they don't hijack your affiliate links either.
You could probably get a complete URL of equal or shorter length though because your new shortener domain could start counting from single-digit IDs again. Bit.ly is up to 7 characters.
