What fan are you referring to? Is there a need to cool or balance the room?
Moving air can aggravate any allergies to airborne particle, could be simple dust or any fine particles. Same in all weather conditions. Are you in an area of the country that requires heating this time of the, e.g., most of the USA.
Sleeping with the mouth open could be due to nasal congestion, can she breath freely through her nose?
Being around a heavy smoker who is smoking when present, is unhealthy... the bad news of "secondary smoke" will generally accepted as fact. While it remains unlikely that exposure to second hand smoke is the problem, the more the exposure the more likely it is related.
As she has undergone surgery there must be a doctor familiar with her and her condition, what does he/she advise?
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