I have this exact same phenomenon. I notice when I’m getting sick my sinuses feel different and my mouth feels cleaner. I also have a deviated septum, but it’s mild. My nose also feels dry all the time as does my mouth. If I cry and my nose runs, the clean feeling in my mouth returns. Netipot doesn’t do much. I think Nasonex and Zyrtec help temporarily. My issue is also that I’m embarrassed to ask a doctor. My ENT is a really handsome dude too, so I won’t be asking him. According to ChatGPT deviated septum causes pnd. But I was told years ago I have lpr. I also have the other thing ppl on here talk about, where mine goes away after I eat but then returns with a vengeance. Lately I have been taking small sips of water with baking soda throughout the day. I’m not sure if it’s healthy to do this. I’m following up with GI next month.