Trying to add a light at the end of a 3-way switch
Good grief, nobody could expect to understand that tangle of red, black and white.  Let's get some red and purple tape and actually mark the wires for what they do. 



Well that's a lot better.. White is actual neutral.  Black is actual hot.  Red is switched hot.  Purples are 2 messengers - they're the same, so there really isn't any need to distinguish them from each other.   

I didn't color your extra wires.  Can you see a bit better how this is going to work -- or to be more precise, not work?  

The original lamp is getting its switched-hot filtered through another lamp.  This is called putting them in series.  They're not designed for that.