How can side effects from medicines taken for asthma affect learning?

It can affect fine written motor skills due to the trembling that accompanies most inhalers that open the airways.

The main way that asthma itself affects learning isn't from medication, however. It is from the number of school days they miss. They miss days due to asthma episodes, illnesses, doctor's appointments, sleepless nights (that are often, but not always, due to medication), etc.

My daughter was a moderate to severe asthmatic, leaning towards severe, from birth to now when she is age 21. She would miss up to 1/3 of school days. She would, at times, have to have home tutoring provided by the district.

Hope this helps!
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Asthma itself, as well as its treatment, affect learning. One can not concentrate mentally, or focus visually, if you are short of breath or gasping for air. Medications, such as bronchiodilators, affect each patient differently. They may relieve bronchiospasms and bronchiocontrictions, but possibly add a narcotic effect to some students. It may be difficult to distinguish such a narcotic effect from the shear exhaustion following an attack, since both cause one to be weak and even sleepy. However, the alternative of severe prolonged or multiple asthma attacks is not an acceptable alternative form either a health nor education viewpoint.

Especially this time of year I have bad allergies that combine with my asthma giving me monster headaches. That's not really from the meds per se. But that makes it very hard to concentrate. Some asthma meds can make you tired and should be taken at bedtime. Also, like others have said some inhalers made me shake and my heart race. I finally found one that doesn't do that.