Is it called a dead pixel if there is a vertical line next to laptop screen?

No, a dead pixel will be only a pixel
By the way, Are you using a Toshiba?
My Laptop got the same line and in a research I read that they produced "defective" LCD screens and they will fix that if you have warranty, else you will probably must change the screen through another tech.

You can try checking by connecting on another monitor to see if the line is still there, if it is there, its Graphics/Video card problem.