Maybe you're having nosebleeds. They're not always gushers, sometimes it can just be a little seepage. It would end up down your thoat. Many people have veins too close to the surface (in their nose) and dry conditions can cause them to crack and bleed. I have had this problem since childhood. I run my humidifier 24/7. The doctor suggested putting a thin coating of vasoline inside my nostils (to maintain moisture) but it numbs my sense of smell so I just live with the nosebleeds.

Diet has a LOT to do with dry mouth, especially when you start to get some saliva production back. Salty foods such as chips, pizza, Chinese food, many soups, etc. will make the problem much worse and hydrating yourself doesn't completely solve the problem either.

Another angle is that you might be a "mouth breather" and that will cause a lot of dry mouth problems as well - even in "normal" persons.