DesignerFlyGirl No, the Store information doesn't sync with the EA App. You're supposed to get a code for your purchase, which you can take to the Store site and register (the Redeem a Code button at the bottom of the page). However, some codes bought through the App show up as used, as if the App did register them for you without actually adding the content to your Store account.
Before doing anything else though, please check Dragon Valley's product page to see whether you can download it from there. Sometimes worlds show as owned in one location but not the other.
https://store.thesims3.com/dragonvalley.html
If the world doesn't show up, look for a code in your email receipt. If you don't have one, or it shows as used on the Store site, you'll need to contact EA customer support for a refund.
https://help.ea.com/en/customer-care/
It would be best to speak with a live person, so you can explain the situation. If you don't see the option, try a slightly different category of issue. In the conversation, it may help to link the master thread for issues registering or installing Store content.
[Current Issue] Sims 3 Store world can't register/install | EA Forums - 11143823
For future purchases, it would be best to use the website rather than the EA App.
https://www.ea.com/en/games/the-sims/the-sims-3/buy/addon/the-sims-3-dragon-valley-gold-edition