Well, for your situation, there are some ways you can have a try. For example, you can use bleaching cream, which contains the active ingredient hydroquinone from a doctor's prescription. First, you can put the bleaching cream onto a cotton swab and rap the dark pigmented area of your skin. At this moment, you should remember to get the cream on areas that are not dark, because it will lighten your skin. Doing this for a while, and repeat it. And then, you can find the result. Besides, you can drink more lemon juice, olive oil which can be good for your eyes. Also, there are many other factors that can cause dark circles under eyes, such as the allergy and alcohol, lack of sleep. For your situation, lack of sleep is the big problem. So you should also pay attention to it. If the situation is serious, maybe you can go and ask the doctor to help you.
Usually, most light based treatments can remove age spots and also target the normal pigment in your skin. That is to say, you may take light based treatments to remove your dark circles caused by hyperpigmentation. But, you'd better see an doctor to get it checked. And you can consult your doctor if light based treatment are available for you. Best wishes.
You can remove dark circles by taking following diets. First, eggs, because eggs are rich of protein, which promote the rebirth of cells, so eating eggs has certain effect of removing dark circles. Lean meat, marine products also have protein, but as the components of the protein of eggs are close to the human body, the effect of intaking it is best. Second, sesame, because it has abundant vitamin E which is good to the eyeball and ocular muscle, hence relieving the dark circles. Third, carrots, because they contain rich vitamin A which keeps the epithelium tissue functioning well, hence helping reduce the pigmentation. Four, kelp, which contains rich irony element. As the irony element is the core component of the hemoglobin, which helps deliver the oxygen and nutrition. Five, drinking green tea helps. Apart from diets, you can do some aerobic exercises to promote the blood circulation, hence removing dark circles.