Orange, While I'm no doc, I can only assist based on the level of care that I have training in. The first bit of advice, don't let any doc diagnose you with Asthma. Doing that puts a red flag on your medical record which then can move over to your aviation governing authority.
Here are some questions I would want to know.
1. How old is your house? When was the last time you had your ducts clean?
2. Did your little one get sick at all?
3. Where is the mucous coming from ? Nasal passage or is it a productive cough ( comes from your chest each time you cough)? If it is coming from your chest what color is it? Is it clear ?
4 Does the wheezing come on voluntarily or upon exertion ( you mentioned you would be sitting, just checking)
5. DO YOU SMOKE ??? Don't lie
6. Are you overweight? Do you feel these symptoms more at night? Are you awakened at night with the wheezing, coughing, mucous or wake up feeling like you are choking ? Are you having any back pain associated with the chest discomfort ? Have you had recent orthopedic surgery?
Alot of questions I know, but that is because it could be anything from allergies to Congestive Heart Failure to Cancer to a blood disorder and back to a simple cold. Hence why you need a full, detailed examination because all those answers can lead to the path a doc will want to take with determing what is going on. From this history, signs and symptoms, he will proceed further with more test. You also need a full lab workup. Pilots try to be alot of things, but having the ability to draw blood from your veins probably isn't one of them
So leave it up to the medical professionals rather than posters on here ( no offense docs!!!). While I would not suspect CHF or Cancer ( again, I've not examined you or listened to your lungs), a PE or blood disorders, I think the signs and symptoms you're having are noticeable and worth seeing someone other than your GP.
Request a chest xray, 12 lead EKG and Echocardiogram. The good part is that you're not complaining of Shortness of Breath. You will also need to have a CT of your chest to rule out a possible airway obstruction. Not trying to scare you but 1. It's not going away, 2. You have a child and 3. You fly. Best of luck and keep us updated.