Is it oversimplification to say sinus infection are either viral or bacterial? can they be both? like existing minor bacterial get worse w virus?

Yes, can be both ; m: Sinuse infection can be triggered enviromental allergy and inflammmation, when cold weather come, our immune system do not work as good, give virus, bacterial or even fungus more chance to cause infection in upper airway, the best way to prevent is to strengthen immune system, hand washing, eat healthy, drink plenty of water, vitamine c rich food or supplement may help to our defense.

Sinus infections: By far the most common cause of sinus infections are viruses. In very few cases (0.5-2%) bacterial infection may follow a viral infection. In individuals with altered immunity we sometimes also see invasive fungal infections. Management conservative (fluids, analgesics, saline drops, decongestants) unless symptoms persist >10d; hi fever (>102f/ 39c) or respiratory symptoms start..Then see ur doc.