That's strange, are you always like that or it happened just now? Maybe you have colds, and you said that it gets worse when your gaming is a thrill, well I think it gets worse because you don't blow your nose when you need to because you are busy playing games.
For your eyes, try blinking, it will help. You are so into the game that you are not blinking hence watery eyes.
Nose? Maybe you are breathing more heavily through your nose, bringing in colder, drier air which causes your nose to react by releasing more moisture into your nasal passages.
I was just doing a search for the same sort of phenomenon that I too have experienced. It begins with my eyes watering after about half an hour of gameplay and then my nose starts running like a mofo.. By the time I've played for about an hour it's like I've got symptoms of a full blown cold with tears running down my cheeks and a snotty nose. It's the weirdest thing. It's most notable in games like GTA, but it seems to happen with virtually every game I play on PS3..which is mostly Call of Duty-type shoot em ups. I'm wondering if it might be the colors in the game, or possibly the game frame-rate? Perhaps the game is slightly out of focus. I just don't know, but it limits my game-play time and is sure a mystery.