It sounds like your areas of concern are on the right track. I am not sure of any really effective OTC meds though. My best recommendation is to find a doc you trust and keep visiting until you have figured out what the underlying problem is. There is always the possibility you have more than one thing triggering your cough. I have had chronic coughs also and I can share some of what I learned througout the ordeals.
My doc informed me that there are 4 main causes of chronic coughs: asthma, acid reflux, allergies, post nasal drip. Pertussis will also cause a chronic cough.
In the past two years I have battled various chronic coughs and I have had to use the process of elimination and testing to figure out the causes. I have asthma, allergies, acid reflux and at one point I was diagnosed with Pertussis as well. One of the worst times of my life was when I had a sinus infection as well as aggrevated asthma, acid reflux problems and Pertussis at the same time. Just as I was healing from those, I also got the flu. My cough lasted from the end of January until about mid-June. (I had 9 doctors visits in the first two months trying to figure out what was going on.)
My primary symptom for all of these conditions was a chronic cough. At times the coughing was bad enough that I couldn't catch my breath and I had aching muscles in my stomach and ribs. My right side was the worst also.
I have asthma that is treated with 3 meds year-round. My primary triggers are allergens, cold air, polluted air and inhaled chemicals. When triggered, the asthma cough can last for quite a while for me.
For the reflux (LPR), my main symptom is just the chronic cough. I don't have any heartburn. Single dose PPI's weren't much help for me. I had a PH test to confirm the presence of acid and was placed on Prevacid 2x/day. This (and watching my diet) has been a miracle treatment for me.
I had Pertussis about 1 1/2 years ago. I had both a blood test and a special nasal swab test done to confirm the diagnosis. Pertussis has the nickname of the "100 Day Cough." Even after I had been treated with the antibiotics, the residual cough lasted about 4 miserable months. I knew I had been immunized against this and was extremely surprised with this diagnosis. I have since found out that the immunizations don't last into adulthood and there is a new vaccine available for adults.
I thought the coughing would never end, but one day I was suddenly cough free.
Good luck finding your answers.