I have dark circles under my right eye but not my left. what could it be?

Allergic reaction: Dark circles under only one eye could be due to an allergic reaction affecting the tissue below one eye more than the other. It could be caused by eye makeup or over-the-counter eye drops, rubbing around the eye can make it worse on the rubbed side. Sleep deprivation will sometimes result in dark circles that can be more noticeable on one side. Excess alcohol intake has been said to cause it too.

Usually, allergies: Only one eye? Ususally rubbing from allergies. Internal diseases and medications would affect both eyes.

Allergy or swelling: It could be secondary to allergy or fluid accumulation under the skin. If you sleep or rub your right side you may causing irritation which leads to inflammation or swelling. Cold compressors over the right eye and attention to the your habit may help to solve this.