I fell a week ago to my left side and i start feeling pain after few days at my chest on the left side specialty when i cough or snizz?

I'm not surprised that you're experiencing such discomfort after such a fall. Contusion of the rib cage with probable associated strain of rib cage muscles most likely occurred. A fractured rib is a possibility but the pain would be quite severe. There is no treatment for a rib fracture and pain lasts weeks. Hold on to your sore rib cage when you cough. See your MD if not gradually improving.