Is there a way to play on my account with my packs on a different computer?

5648969​  It's perfectly possible to use your account on multiple computers, even at different locations.  The EA App shouldn't be switching accounts on you.

Are you trying to launch Sims 4 from within the App, or from a desktop shortcut?  If it's the latter, try pressing Play in your game library.

If that doesn't help, clear the EA App's cache and try again.

https://help.ea.com/en-us/help/faq/clear-cache-to-fix-problems-with-your-games/