Nicisoxx The EA App icon on your desktop changed because it's a shortcut to the actual executable (the file that runs the program), and the shortcut broke. I don't know why, but it happens and isn't a big deal. You can create a new shortcut if you like by right-clicking the EADesktop.exe and selecting Send to > Desktop (shortcut).
To be clear, now you can open the EA App, and it loads properly, as in, you see your library, friend list, etc., but launching Sims 4 from there doesn't work? And is this still true if you restart your computer immediately before you try to play, without opening anything else? If so, let me know what happens in this instance (the "already running" error, a different error, nothing). Sometimes the second attempt to launch the game fails in a different way than the first, and in a way that's not indicative of the underlying problem.
The "already running" error has a master thread with suggestions here:
[CURRENT ISSUE] Sims 4 Unable to Start, Already Running | EA Forums - 11818313
Naomie2003 Anti-cheat has nothing to do with Sims 4, and someone only playing (or having trouble with) Sims 4 shouldn't be installing it.