We did shopping at Cozumel - took a taxi ride from the port down to the end of the "main" shopping strip and went in some shops. Los Cinco Soles was our favorite by far - they have EVERYTHING and an amazing selection/quality. Pottery, jewelry, clothing, alcohol, most all of it handmade - and please buy the biggest bottle of their Mexican vanilla you can. Buy 2 or 3 bottles. That stuff is AMAZING. We use it for all of our baking and ice cream making and it makes a great gift! There is a small version of Los Cinco Soles at the port, but their huge store is down at the end of the main shopping strip - much larger selection. It's very popular and I'm sure if you say the name, people will know what you're talking about. We got all of our souvenirs in that one store!
PS I am an artist - mostly ceramics and painting, but I do it all - and I left there with 3 pieces of pottery. They source things from artists all over Mexico. It takes a lot to impress me. Lol. Good luck!!