Say If I'm running to north at a very high speed. And as I'm running, I'm shooting a beam of light toward west, will the light go completely west, or it will have some degree toward north too?
First, for clarity your scenario doesn't involve "forces", as the term is used in physics.
But to answer your question, from the perspective of someone standing still, they will see the light move in some direction between North and West (That is, they will see the light moving somewhat towards the north, depending on how fast the runner was running).
From the perspective of the runner, he will see the light move directly towards the West.