I have both cough-varient asthma and reflux. My reflux symptom is a cough as well.
My asthma is triggered by environmental factors (cold, pollution, chemicals, etc...) and by the reflux.
The trick for me was finding treatments that work for both the asthma and the reflux and balancing them at the same time. I recommend that you find both a good Pulmonologist and Gastroenterologist. If you aren't comfortable with that route, a good ENT who specializes in asthma and LPR could also be helpful.
Reflux with symptoms in the upper airway and throat is called Laryngopharyngeal Reflux (LPR). You might want to do an internet search on this to get ideas for treatment.
I've had both the reflux and asthma for years. They were treated seperately with changes in treatment as the symptoms changed. A year ago, I ended up needing emergency asthma care. After that, I started seeing a new Pulmonologist. He did some testing and told me that I wouldn't be able to get my asthma under control until I got the reflux under control. That is when I went back to my GI doc. In the meantime, I had various treatments prescribed for the reflux and my asthma treatment was upped. In my case, it took a corabination of asthma meRAB and a double dose of PPI's for the reflux. My case is a bit extreme though. I ended up having surgery to correct the reflux. That was only after the treatments that worked for years stopped working. I did have things under control for about 6 years prior to this.
Some of the tests that I had that confirmed my asthma-reflux problem were: Modified Barium Swallow and Esophagram (these confirmed the reflux was coming up and irritating my lungs), 24 hr pH (confirmed the severity and frequency of reflux), Manometry (confirmed my LES was not working correctly), chest x-rays (ruled out other causes), EGD (verified the reflux hadn't caused esophageal damage yet), Pulmonary Lung Function testing (tested lung functioning and capacity). Also my history was important in the process as well. It was the Barium swallow that really confirmed that the reflux was coming up to my lungs.
Things to ask your doctors about: obtaining an emergency inhaler (such as Albuterol) for breathing emergencies, using a daily maintainence inhaler (such as Advair or Syrabicort), reflux medications (such as PPI's), diet recommendations.
To help with the reflux, there are also other things you can do. Prop the headboard on your bead up by about 6 inches. A couple bricks or some boarRAB can be used. I just bought some bed risers at a local bed and bath store. By doing this, you are using gravity to help keep the acid from coming up as easily. This isn't a cure, but may help some. Sleep on your left side also. Try to limit how much you are bending over and avoid clothes that are tight around your stomach. Every time you scrunch your stomach, it can push the acid up. Watch your diet. My GI doc has me avoiding: fatty, greasy and fried fooRAB, spicy fooRAB (including onions, garlic and peppers), tomatoes and tomato products, citrus fooRAB and drinks, caffeine and carbonated drinks, chocolate, alcohol and nicotine. Through trian and error, you may find other fooRAB that are triggers for you that you should avoid.