Actually first you may wish to see a doctor.  It may be an infection and a doctor would be the best one to decide the course of treatment.  Granted -- the air in Beijing is not clean these days but you have picked up some germs for sure.  In any case, buy a good face mask, the kind that you see so many wearing.

1. Face masks don't work (unless you're selling them), or at least they don't work for more than 20 mins, the particulates in pollution are just too fine, germs and such are comparatively huge compared to the normal pollution particulate.

2. I've heard of getting a sinus flush, don't know what it is and it surely doesn't sound pleasant but ............

3. Keep out of the pollution as much as possible, fit a quality filter system to your air con and use it, remember you don't need to have your air con on cool, just use it as an air filter.

4. Stay away from coughing and sneezing people, hmm, ........................ perhaps move to the moon?

Not sure that what you got is pollution based actually. Sounds like a germ as mentioned. So to stop the snot generation you take Loratidine - available in all pharmacies. The cough is a different matter. Try some Nimesulide but I also suggest that you go to the echinacities article written just a few days ago about Chinese pharmacies and the medication available. There was some very handy stuff in there and of course it has the Chinese names for the medicines. I had a doozy of a chest cold last winter which eventually led me to seek advice at the local hospital (not recommended) and I have another now. Pollution here with the petrochemical plant is...well....defies description but I don't believe what I had was related to that although it certainly doesn't help. My other sense of wonderment is how do these germs survive in -30C temperatures anyway!?