@AxolotlAvery An audio clip of the sound probably wouldn't help here. Instead, open the case of your computer, and load the game with the sound muted. (You can use the Windows sound option in the lower-right corner of the screen.) When you hear the sound again, put your ear right next to your computer case and see if you can tell where the sound is coming from. Pay particular attention to the graphics card, if you have a standalone GPU: it has its own fan or fans that might need maintenance, and it also has other internal components that sometimes emit a high-pitched whine when under stress.
I doubt that switching from ethernet to wifi had anything to do with this, but you could have accidentally bumped the computer in just the wrong way when you moved it. Still, if you want to make sure, try disabling wifi. You can sign into Origin and put it in offline mode before launching Sims 4.