From your description, it seems that you got wrinkles under the eyes. And wrinkles are the natural process for human beings. Personally, the best and simplest way is applying anti-wrinkle cream for the skin under your eyes. Besides, you shall also keep healthy life style. For example, you shall go to bed eerily and get up early. Keep health diet include taking more vegetables and fruits daily. Also, do some exercise is good for your body, also help reduce creases under my eyes. Hope this may help you.
Since there are so many home remedies for you to choose, I will tell you some that I usually use. You can try to do some facial exercises, which is not only good for your eye wrinkles but also good to your facial skin as well. This is a good way that really worth trying. Wear your sunglasses when you go out even in sunny days. Trust me, this can help you prevent uv rays from attacking your skin and naturally it can reduce the wrinkles under your eyes. Furthermore, you can also try grape seed oil, this can also be very good for your skin.