Yes, air conditioning can affect people’s sinuses for a couple reasons.
The first being that cold, dry rooms trigger runny noses the same way going outside in the winter after being in your warm house does. The sudden change in temperature and humidity triggers glands in the nasal membranes to produce mucus.
Additionally, tiny particles such as pollen, mold spores, and dust mites can get lodged in an air conditioner’s filter which are then distributed through the air once it’s turned on, causing anyone with allergies to have a reaction.
Bottom line- regularly changing your air conditioner’s filters can help reduce the second issue but nothing can help the reaction from sudden changes in temperature and humidity.