I have stopped working on new products and switched to work on my website which is under construction for years now. After trying to promote my works purely through my FB page, I came to the conclusion, that this path doesn’t work well. IMO, you definitely need a website if you want to seriously promote your works (or referred third-party products).
Having a website offers many advantages: you can design it so it fits perfectly your niche and audience, you can optimize SEO, you can organize and showcase your products at will, you can redirect your visitors to Zazzle’s local domains without losing affiliate revenue by customers switching to a different domain directly on Zazzle (your affiliate ID is not forwarded in that case), you can make your own mockups, you can offer additional info and services, your links on socials will be shorter, you create your own brand, etc.
In terms of SEO, pages with tons of product links are not the best choice, because search engines rely on content those days, and having tons of different products with different short texts on the same page equals having practically no dedicated content the search engines can use to optimize their results. Plus you can’t write strong metatags because the content is widely spread.
What you should do - and what I’m doing - is to create specific product pages, such as “Fleece blankets”, “Pillows”, “Mugs”, etc., fill these with a suggestive banner (for your visitors’ eyes), a product description (both for your visitors AND search engines), product-related meta tags and finally with the related products linking to your Zazzle product pages (better if done with your own mockups and short description but also viable through direct linking/sharing from your Z’s product page). This way, you give the search engines product/niche-specific content and keywords, and make it also easier for your visitors to navigate, besides incentivizing purchases with a beautiful presentation. Adding also themed pages, e.g. for holidays and occasions, gift ideas, etc., and creating collections will improve your chances of success, too. And if you use Pinterest, a website comes in handy, too.
The drawback is, it’s a whole lot of extra work you have to deal with. But it’s worth the effort, IMO.
Good luck!