The symptoms can be different for every child and elusive at best. If allergeries are contributing to your son's asthma he could have multiple allergies layering up the stress on his poor little immune system. And, wow, is there a lot of snake oil for sale to desperate parents looking to help their children!
We finally unlocked our child's major allergies that were causing eczema and possible cold enduced asthma through results from a blood test (ask for a copy of the detailed results and question everything) and working *extremely* diligently with a dietician on an elimination diet.
Our experience with doctors is that they focus on treating and controlling symptoms, but don't seem as interested in uncovering the causes. I don't blame them...they are looking for an undetermined number of needles in a haystack and then depending on parents to remove them from the child's diet or environment.
It was literally a full time job to figure out our son's allergies. I was glad I no longer worked, because if he was under someone else's watch during that time, we would certainly still be struggling to keep his eczema under control.
The most difficult change we made was finding our dog a new home and replacing our furniture. Multiple ouches. Our son has dog a allergy and it wasn't enough to keep the house clean and the dog out of his room. We know people who refuse to say goodbye to their dog and their son is suffering. They are crazy. After seeing the dramatic change in our son, I feel very strongly that no pet is worth sacrificing your child's heath. A child's home needs to be a safe place where is allergies aren't constantly on overload. If it can't be his house, at least his bedroom so he can sleep in relative peace.
Best of luck to you and your little one. Asthma is frightening and I hope you are able to get it under control.