Is it possible for asthma to trigger skin abnormalities?

Unlikely: Asthma is a lung condition with mucus production, airway twitchiness, swelling, and inflammation that has symptoms of cough, wheeze, chest tightness and/or shortness of breath. No particular skin abnormalities are triggered by asthma, although patients with allergic asthma may have other atopic conditions such as eczema (atopic dermatitis).

Maybe not, however: In many asthmatics, allergies are the trigger that causes attacks. These same allergies can cause skin rashes, etc. Best to be tested so that you can at least try to avoid the things that are causing your asthma nad rashes.