No, it is not normal. You'd better go to see the doctor and find the exact reason. The dark circles under the eyes are usually caused by the lack of sleep, not good blood circulation and so on. Running will not cause the black circles under the eyes. You'd better go to check it and find the good way to reduce it.
We would simply not have dark circles after running on the playground. So, I mean, it that temporary ? If you constantly find dark circles after taking sports, there must be something wrong with your health. Generally speaking, sports would not lead to dark circles. Therefore, I recommend that you try to take a medical exam and take measures to fix your problems, also try to develop good living habits.
Well, yes, it is normal to have dark circles under your eyes after you have the running. As we know that there are many reasons which can lead to dark circles, such as lack of sleep, hereditary reasons, even stress, fatigue. So when you have running, it will just make you feel tired, and stressed. At that moment, it will just affect your eyes, leading to dark circles. To treat it, there are some ways you can have a try. You can use some cool cucumber slices. As we know that cucumber slices have long been used to reduce puffiness and refresh the appearance of skin around the eyes, providing a fast "pick-me-up" for tired and puffy eyes. But on the other hand, they can also be good for the dark circles. So just put a slice over each eye, extending over the darkened area. Remember that you should do this everyday, coupled with lying down for 10-15 minutes. And that can be effective.