Would a nebulizer have helped me during my asthma attack as a result of an allergic reaction to taking aspirin?

Yes, likely. Asthma attacks triggered by Aspirin can be severe and life threatening. Albuterol administered by a nebulizer or through an inhaler (with good inhaler technique) can help with bronchospasm (cough, wheezing, chest tightness). It is imperative to avoid all Aspirin products and nsaids like ibuprofen. Some medications like montelukast can be especially helpful for Aspirin allergic patients.