**Adding this: If a person has Asthma, only a professional can accurately diagnose it, and whether or not it is a mild form or not. My Asthma is "mild"... BUT, there were many times, that I had had, emergency acute stages of it, too. AND there is no way, to predict that, if/when it does develop into a worse stage.
Not all inhalers, have those same side effects you noted. There are many types of inhalers. And each individual person, reacts differently to it. My Mom has an inhaler, that works for her. For me, I don't like it and have another type. For example.
My Mom, developed Asthma... later in life. BUT prior, she had had Bronchitis etc. and one time she didn't go to the Doctor to treat it right away, and now she has a scarred lung. Lung damage.
So, being your son is having coughing fits... I would seek another specialist, a Pulmonologist for example, and see WHY he is coughing so much. And whether or not it is Asthma.
It is not always good, to compare one's Asthma, to another person. Because each person, has it differently, and per acuteness which cannot be properly evaluated unless it is by a professional.
And if he does have Asthma, medication... is... necessary.
Untreated Asthma, can also create, other medical problems and emergencies. As, Riley J. noted below.
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I have had Asthma since I was a kid.
As an Adult, I now know a lot more about MY asthma.
I don't use my meds everyday.
In children, Asthma can manifest or display, differently. Not in the conventional "wheezing" manner.
Each person's Asthma, is different.
Attacks can come on suddenly with no warning.
My Doc, said that people die from it. They didn't have their inhalers on them, or waited too long until going to the Doctor.
Now, you saw an Allergist.
Not a Pulmonologist.
Get a 2nd opinion as well.
I would, get an inhaler to keep on hand.
There are MANY different types of inhalers.
For maintenance or rescue types.
The side effects you listed... mostly occurs when the inhaler is given but is not used as directed. Because, a person can overdose with misuse of an inhaler too. That happened in my State, to a Tourist.
Again, get a 2nd opinion as well.
Remember:
Asthma, is not just about wheezing or coughing or gasping for breath. By the time someone is gasping for breath anyway, it can be too late and they can die. Or their skin/lips/nails will be all blue. Because they are suffocating.
THE point is, a person with Asthma.... will have (especially in acute stages) inadequate Oxygen levels in their system and blood. And their chest will be sucking in, each time the take a breath. And by this time, it is in an acute stage.
Even having acute coughing fits.... can cause stress on the heart.