Junan and KRae are correct. Install order doesn't matter anymore.
You won't loose any of your saved games either. As the installed game files get installed in a different place than where your saved games or user files are located.
Here's a little more of what I'm talking about:
User files should be located here:
--
\Documents\Electronic Arts\The Sims 3
\Documents\Electronic Arts\The Sims 4
==
Game install files should be located here: (by default)
--
C:\Programs(x86)\Electronic Arts for the DVD Version
C:\Programs(x86)\Origin Games for the Download Version through Origin
If your user files aren't in your \Documents\Electronic Arts\ (Sims 3 or 4) folder, move them from where you found them into one of those folders. As that is where the game saves the user files by default.
If you are still having problems finding your Origin games it may be best to
contact EA for further assistance.