The masks are actually usually worn by the person who is sick, not to prevent getting sick. And they dont (rarely) take sick days, so they wear it and continue to work.
I think a lot of foreigners and locals get sick in winter in japan, fast changing seasons and really huge pollen counts so a lot of people get hay fever in Japan when they normally wouldn't too.
Vit C and water. Same when Im trying to kill a cold off (like today). Water, up to 2000mg of vit c (only when I actually have a cold) and keep warm!
I used to get colds a lot, but now I very rarely do, usually self inflicted. Like eating a high gluten meal when I know I shouldn't. SO thats another thing to look at, any allergies that might be lowering your immune system.