See what kind of blue birthmark it is. There are also many kinds of green birthmarks, which need to be diagnosed clearly before the right medicine is given. Commonly known as green birthmark is Mongolian spot, which can fade naturally. Ota nevus, laser treatment is very effective. Pigmented nevus, there is no good way, only surgery, milk coffee spots, laser effect is also acceptable. I suggest you go to dermatology or plastic surgery first.