You don't have the most obvious symptoms of acid reflux, but you should not discount reflux as a possible cause of your symptoms. By one study's estimate, 40% of people who have a persistent cough that is caused by reflux have their cough without a sour taste and without heartburn.
Your symptoms don't give us obvious clues that direct us to one of the most common causes of a persistent cough. A cough that has persisted for longer than 8 weeks should be evaluated by your doctor, and it is reasonable to have a chest x-ray.
Your cough could be coming from one of the common causes that we have already reviewed, even though you don't have obvious associated symptoms. This is true for most people who have a persistent cough. Among non-smokers who have a normal chest x-ray and who do not take a medicine in the ACE-inhibitor group, 99.4% of persistent coughs arise from either post-nasal drip (or other upper airway irritation), asthma, or GERD (reflux).
You and your doctor can consider treatments for one or more of the common causes to see if your cough improves. Your doctor can also consider rare causes of a persistent cough, with a complete physical exam and additional tests if these seem reasonable.