Can a person have an asthma attack without feeling breathless and no wheezing. can the only symptom be coughing?

Yes and no: There are those with mild asthma (cough variant) that can have coughing spells that respond to asthma rescue inhalers.These patients rarely but can wheeze. A chronic night cough may be their main symptom. I wouldn't call this an asthma attack, although one might start this way.This level of symptoms cannot be considered it's equal.Most with this variant never have a significant attack.

Yes: Common for asthma to present as a cough and not wheeze, in a person who has asthma. You have to treat a cough like you are wheezing, especially in children.