The mucus may be a residual of inflammation of your nose and/or sinuses that occurred along with, or due to your acid reflux. If the former, it is not at all uncommon for a condition of excessive mucus to persist for many months. If due to reflux, it may take 1 to 2 months to get maximum effect from the anti-reflux medicine.
Even i faced the problem of sticky mucus coming to throat after eating for the past 1.5 years . IT is highly irritating and i had almost developed an aversion to food and then lost weight.
Actually problem is related to wrong digestion and wrong respiration. If food is not properly digested then it gets converted into phlegm and affects the body as a whole.
In general the ayurvedic treatement and yogasanas(YOGA) helped me a lot.
There is however certain discretion in doing the yogasanas that must be followed :
If you are overweight then you should do mosttly forward bending asanas. Also you can do the pranayamas(breathing exercies) that involve more exhalation exercises like : "kapalbhati pranayama" . You can take a hot water bath.
If you are underweight and malnourished then you should do backward bending asanas : (eg: bhujangasana, ushtrasana). And pranayama that involves internal retention of breath : antar kumbhaka/sitali. You can take a cold water bath.
Try to be out of AC and breathe in the fresh natural air outside.
The yoga must be done under expert advice and guidance and improper practice can be harmful, but with proper practice you can use it for your own benefit. Yoga treatement is long time one but gives sure results.
Also eating habits should be such that you do not overload your digestive systems , too much of chocolate, cheese, mayoneise, pastries is not good. Instead fruits should be amply eaten. Also one should not over-exercise as it burns out the tissues.
All in all a "balanced" diet, exercise, behaviour and meditation will help a lot. Remember, the body has a great feedback mechanism and if you listen to it and alter accordingly then it will respond well too.