SoireeSenpaii Let's make sure the graphics driver installed properly. Click Windows key-X, select the Device Manager, expand Display adapters, right-click the Intel HD entry, select Properties, then Driver, and you'll see a version number. Your old driver version was 27.20.100.9664; the new one is 31.0.101.2140. Don't worry if there are more or fewer zeroes in the driver version you see, that's normal. If the driver didn't update, try installing it again, and if that still doesn't work, stop here and let me know.
If the newer driver is installed but doesn't help, please try playing in a clean user folder. Move the entire Sims 4 folder out of Documents > Electronic Arts and onto your desktop. If it copies instead of moving, or you get an error when trying to move it, stop here and let me know.
Otherwise, when you launch the game, a clean folder will spawn with no content. (Your saves and other content will be intact in the folder you've moved but temporarily unread by the game.) Don't add anything to the new folder yet; just start a new save and see how it runs. Let me know exactly what happens this time around.