Burn around nipple after laser hair removal, will it heal on its own or should I see a specialist?

You should return to the doctor's office so they can see the result, advise treatment, and adjust the settings next time.  Keep the areas moist with a product such as Aquaphor and avoid any sun exposure or tanning.

With any burn from a laser or light treatment it's necessary to keep the area moist. I would suggest you return to the office that treated you and see the physician who oversees the treatments. It will heal, but it will heal better if you see an expert who can advise you of what will be best in this situation.