When the existing space is minimal, we have to invent, like turning a mini hanger into a Necklace Organizer. This is a simple idea, and you will probably only need to buy a small package of little cup hooks. I glued the hanger to the inside of my wardrobe, but you could use those "Command" hooks, or double-sided tape, or hook-and-loop tape. If you want the hanger to be mobile, simply hang it on a small hook or screw you install.
This Necklace Organizer that makes great use of small spaces!
You can also adapt this idea to hold earrings or bracelets. Perhaps make a hanger for each type of jewelry!
Now that you've got a way to organize your necklaces, you need to make some Porcelain Jewelry! If you've outgrown the single hanger of hooks, try making a low-profile Jewelry Armoire out of pallet wood!