@indycutie Again, I was not suggesting that rotating the camera was causing the problem. I was asking if rotating the camera changed the result you were already seeing. So please let me know either way.
There's no reason to uninstall and reinstall the game. Instead, if restarting the game after changing the resolution doesn't help, and please test that first, move the Sims 3 folder out of Documents > Electronic Arts and onto your desktop. When you launch the game, a clean folder will spawn with no content. Load the game to the Main Menu, change the resolution to 1600x900, quit, reload, and see whether this happens in a new save.
If the new save is fine, copy your existing save to the new folder, but nothing else yet, and test it too.