Has your doctor run any tests to rule out various causes, or did he/she just do a physical exam and prescribe medication?
CA125 is a marker test for ovarian cancer, no? C reactive protein increases when there is too much inflammation in your body. Kind of strange tests. And both were normal.
So, what about a simple virus? You know that medication isn't really going to affect a virus, it has to run its course. Coughs, phlegm are normal with a virus.
Silent acid reflux is what they are worried about or you are worried about since you bring up gerd? It can cause a cough, wheezing and sore throat. But since these symptoms are new, I'd be more inclined to suspect a virus? And you can get a temporary asthmatic condition after being sick which is maybe why you are not in need of a chronic asthma inhalers?
Here is information on gerd https://www.webmd.com/heartburn-gerd/guide/understanding-gerd-symptoms You'll see a cough can be a symptom.
When you say you have intestinal gas, do you mean flatulence or burning sensation?