TheSimMommy You don't need to sign into the game in order to use Store content. If you can't download your content through the Store site, try a different browser, for example Firefox generally works well with the Store site.
Another option is to use the item's product page rather than your purchase history. If you see the "you don't own this item" error, refresh the page and try again. Here's the page for the carousel set:
https://store.thesims3.com/setsProductDetails.html?productId=OFB-SIM3:72712
For the world you purchased, please also see the first post of this master thread:
Sims 3 Store world can't register/install | EA Forums - 11143823