What is the chance that blue skin is caused by asthma exacerbation in children? what are the usual symptoms?

Unlikely: If an asthma attack is very severe it can lead to respiratory failure where, the oxygen level can decrease and lead to cyanosis (bluish color of the lip and around the mouth). This is a very late sign in an asthma attack and an emergency. The usual signs of asthma in children is relentless cough, wheezing, shortness of breath/difficulty breathing.