What's the best solution for the dark circles .could allergy increase the dark pigment around the whole eye circle since i have running nose all times?

Yes: Allergies are known to be a common cause of dark circles under the eyes, due to vasodilation of blood vessels from histamine release. It's best to see an allergist for skin testing. Common allergens include pollens, dust mites, molds and animal danders. Based on the results, the allergist can usually help you feel and look better if you are allergic.