Yes, sinus infection can cause the appearance of dark circles under eyes. Because when you get cold, the pressure inside the blood vessels will increase, slow down blood circulation and make skin paler, the dark circles more distinct.
There are some treatments to improve the dark circles.
1. Cold/hot compress of eyes. Put two towels in a cup of warm water and a cup of iced water separately. After applying one towel cover eyes for 5 minutes, apply another towel for another 5 minutes. This can stimulate blood circulation.
2. Potato eye mask. Slice potato, and cover it on the dark circle. Potato can lighten the color of skin.
3. Drinking clear/mineral water instead of coffee. Water can facilitate the toxins elimination.
4. Applying concealer to cover the dark circles.