Could my visible artery and pulse on the left side of my neck indicate swollen lymph nodes or a tumor in my neck ?

Easy does it, Steve: Most people have a visible vein on each side of the neck, especially when they're lying down, and most people's carotid arteries are visible. These have nothing to do with your lymph nodes. Do you have palpable nodes? A palpable tumor? Is it possible you're just physically fit and your neck structures are thus more visible? The vast majority of swollen nodes in a young guy like you are harmless.