Q:

May we use "Neither" without "Nor"?

I neither use whatsapp nor facebook

OR

I don't use whatsapp neither facebook  

Is second example correct?

A:

Your second example isn't correct, but you can use "neither" without "nor", if you are not explicitly naming both alternatives. 
For example, if someone asks you, "Do you use Facebook, or Whatsapp?"
you can answer
"I use neither." or "No, neither one."

