There is congestion in those little veins in the mucosa lining the nose. This increased venous pressure backs up the venous circulation connecting with the nasal vein network. That network includes veins around the eyes and the middle of the face, not just inside the nose. So, plain old sinusitis can do it. A bad cold can do it.
Chronic sinusitis can produce chronic puffiness.
Some of us have dark circles and puffiness not because of anything wrong, by the way, but just because of the details of how we are constructed. This can be inherited.