Well,
I will start off first by stating i am not a doctor,so you can take my advice as you wish.
Ok,the a/c may be the problem,the cold air you breath in at night will dry your sinus passage's
out making your system vulnerable to mucus formation(bacteria).It depends on what is going on
with you,first,answer this,how long has these symptom's been present? First,let's distinguish a few
things,When you say"cold" that will intel a fever to go along with it,do you have a fever?
If not,then if you are spitting up any green mucus,then you might have an upper respiratory
infection.You have to go to the doctor,they are the only ones that can give you a full diagnosis.
But i would not sleep in the a/c anymore.
Maybe move it away from you so you are not directly up under it.Run a vaporizer to moisten the air in the room.Also,you mentioned dust?Well,you need to dust and clean the place properly,breathing dust particle's can make you end up with the same respiratory infection.If you are having green mucus,spit up as much of it as you can,drink plenty of hot green tea with honey.Tea is a natural property that has antioxidant's in it.Honey helps coat the throat.
If there is mucus present,when you lay flat on your back,the mucus drips backward's on your lung's,that's what causes you to cough until you are chocking. Sleep sitting in an upright position until the wheezing and coughing subside's.
I am talking like almost upright,but with a slight slant,think 2 pillow's high,or 3 depending how thin or fat they are.
You should re-think your pillow's as well.I would get a case cover to put the pillow's in to protect yourself from bug's and mite's.Make sure you are cleaning your sheet's/pillowcases at least once a week,i suggest going with all cotton,making it simple and easy to clean.
During a cold,feed your body good thing's like hot chicken noodle soup,orange juice,tea w/honey,and sugar free cough drop's.I have also tried Mucinex,it is over the counter.I did use it one time with success.But i was like you,i liked to sleep in cold room's,so that was where the problem was lying.Like i said,i am not a doctor,you take this advice to your own choosing,good luck,and if it persists over 10 day's,get to the doctor!!