IZZYCORNN The "My Library" section of the Gallery is actually what's stored locally on your computer, not anything online. This includes Gallery downloads as well as creations you've saved without uploading them. So this data wouldn't show up on your new computer.
If you still have access to your old computer, copy over the Tray folder, in Documents > Electronic Arts > The Sims 4. Put all the files directly inside Tray on the new computer, and they should show up in-game.
Your custom content would be in Mods, of course. If you don't play with or alter the saved households until your cc is loading again, the sims should still be wearing their old cc.