EA app will not download my expansion pack

Hi!

So I had the exact same problem as you and spent ages clearing caches and changing my user access control settings and all this other stuff. In the end what worked was not to do it from the expansion pack store page (for me it was Growing Together) with the big download button, but instead through the library. So I clicked Library (for me this is on the top left of the EA play window) and then under 'Installed' the Sims 4 should be listed- it's a big box with the Sims 4 picture in and a small play button in the bottom right corner. In the top right corner of the Sims 4 box is a little grey box with '...'.  Click that, click Manage Add-ons, and then the new expansion pack should be at the top with the download button next to it. I clicked that one and it finally worked. 

Sorry if that was more detail than needed but I wanted to be super clear, I was getting really frustrated myself aha. I hope this works for you!