I have a small visible vein on the left side of my nose that throbs , it kind of hurts and gives me headaches is that normal ?

No: If it throbs , it is likely a small artery. If you suffer from migraine, it is possible, but unusual, to find it throbbing during an attack .But if it is a constant problem, then you really need to ask your doctor to take a look at it.

Nasal veins: Nasal veins are very common and there are mutiple options for treatment including sclerotherapy, ipl, laser, veinwave, veingogh and micro needle radio frequency. The size of the veins and the training and experience of the treating physician usually influence what treatment is recommended. My usual treatment is sclerotherapy or laser for very small veins. You should see a vein specialist.