I am so sorry you are going through this. My heart goes out to you and your little one as I know this is a scary time for you. When my son was a baby I had him in daycare. He was always wheezing, coughing, full of mucus. He was diagnosed with asthma and sent home with a nebulizer.
I couldn't cope. I didn't want my baby to live on meds, so I left my job to take care of him. Miraculously he was better as soon as I stopped taking him to daycare.
I know it's unreasonable for every mom to quite her job and stay home. This may not even be your situation. However, you may want to look at your little one's environment to identify a possible cause. Could it be something in the air? Allergens? Products or chemicals used in his surroundings? Food or pet allergies?
If it's on going it sounds like it could be an environmental reaction and, yes, possible asthma. I am not a physician and I am not in any way making a diagnosis. I am just speaking from experience.
Wishing you the best and hoping your baby feels better soon.
It's unfortunate that doctors are not spending adequate time with patience to properly diagnose.