Hey Julien, sorry for the mishap! My first guess would be that maybe you're logged in with a different Adobe ID on your computer. Try logging out and logging back in! The other option would be that you accidentally purchased a mobile-only plan instead of one of the Rush plans that allows you to sync with other devices. You can double-check on your plan here: https://account.adobe.com/plans
Let us know if this helps! If you want help making adjustments to your plan, you can DM us on twitter.com/adobecare or start a chat using the 💬 icon in the bottom right of this page: https://helpx.adobe.com/contact.html
We can't help you make adjustments here on the public forum because we don't want you posting your contact & payment info for everyone to see! For privacy, please use the two options above.