The cough when you're in air conditioning could be your airways reacting to the colder air, especially if you are sitting right near the a/c vents. if you're sitting near the vents, the air blowing could also be drying out your airways, which can cause you to cough.
As for the vitamin C in the foods such as lime, oranges, etc. - my guess is that it's more related to the acid in those foods causing the cough. Acid reflux can cause cough and you can have acid reflux even if you don't get heartburn.
there are many causes of cough - acid reflux, asthma, reactive airway disease, bronchitis, pneumonia, allergies, etc. and as I mentioned, a dry throat can also cause cough.
I would definitely suggest keeping your throat as moist as possible, especiallly when you're in air conditioning - drink lots of water, tea (although be careful with teh amount of caffeine you're drinking because caffeine can also dry you out, causing a cough), fruit juices. When you're inside in the a/c - sit as far away from teh vents as possible so that the cool air is not blowing directly on you.
Do you get any other symptoms when you eat the foods that cause the cough, such as itchy throat, swelling in the mouth or throat, hives, itching, etc.? If so, it's very likely that something in the fruit you are allergic to and you may want to consult with a doctor to determine what your allergies are.
Best of luck!