UPC Question for Product Bundles

Hi Everyone, I’m just getting started selling on Amazon. If I create a bundle of two products that I also sell separate, I think I need a unique UPC for the bundle? Do I need to have new labels made for each product in the bundle with the bundle UPC, or can they ship with their original UPCs and have the bundle UPC on an outer product package?

For example, let say I sell shampoo with a UPC of 123 and I also sell conditioner with a UPC of 456. I’ve decided to also sell them as a bundle. The bundle UPC will be 789. I plan to shrink wrap the shampoo and conditioner together and put the bundle UPC on the shrink wrap.

Do I need to have new labels with UPC code 789 for the individual shampoo and conditioner bottles that I plan to bundle or can I use the existing labels with the shampoo UPC 123 and conditioner UPC 456 and just have the bundle UPC on the outer shrink wrap?

Thanks in advance for your insights!