My eyes have dark rings on under the eye as well as the eyelids. is this reason enough to go to the doctor?

Not necessarily: The discoloration may just reflect a slowing of blood flow in the rich capillary bed of these tissues. This can be triggered by a reaction to airborne allergens that enter the eyes. If true your eyes may itch & have clear drainage. If you otherwise feel fine I don't consider this a sign of some worrisome illness. If you are worried about other issues schedule a visit.