Does every nerve ending send information to the brain separately?
There are two main structures in the human nervous system: 


The central nervous system, which includes the brain and spinal cord 
The peripheral nervous system, which is all of the nerves in the rest of the body (fingers, arms, feet, etc.)  


  

The signals taken by the peripheral nerves mainly travel to the brain through the spinal cord, and the brain sends signals back to the peripheral nerves through the central nervous system.  

There are a lot more complex mechanisms and various exceptions, but essentially: the nervous system is a vast network of signals, and the majority of these signals travel through the spinal cord to the brain and from the brain to the target nerves. 

The signals travel via different nerve "branches" — think of it like a tree of nerves, with the common root being the brain.  

For more information please see: 

Overview of the nervous system for dummies  

Wikipedia (with strong references and lots of detailed information)