My sinus problem was reduced when I got myself an air purifier. It still gave me problem on certain days, but definitely better than having to wake up daily with congestion. This was about 8 years back. Finally decided to see specialist when I discovered I could use my insurance to cover the medical cost few years later.

I sleep with windows closed and fan switched on. I don't really use aircond when sleeping, but on those rare occasion, I will have both a/c and air purifier switched on.

Leaving the windows open while air purifier is running would be pointless, unless you are able to filter the outside air. What I will do is to open the window when I'm not in the room or when the purifier is not running.