Hello, not sure if you are on any medications but if you are some medications can cause a chronic dry cough (some sort of allergic reaction). My mother in law suffered from this for about a year. Doctor couldn't figure it out until one day she thought maybe it was her blood pressure medication so they changed it and the cough went away. Just a thought.
you take ginger and lemon and cut in small pcs and take one pcs ginger after take your meal.
There are 3 very common reasons for chronic cough -- GERD (reflux), asthma, and post-nasal drip. It sounds like yours may be post-nasal drip, given that it is worse at the end of the day and better when chewing gum (you make more saliva and the back of your throat stays wetter). I would recommend trial of an allergy medicine or nasal spray.