Is it necessary to consult even if she doesn't have a fever? How normal is it to cough like this? She's not so bad during the day...

It is important to consult a doctor even if there is no fever. Coughing can be a sign of an underlying issue, especially if it is severe and persistent. It may be helpful to have a plan of action from a doctor for managing asthma symptoms. If symptoms worsen at night and necessitate the use of a rescue inhaler, it may be a sign that the condition is not well controlled. Consider seeking a second opinion from a medical professional if needed.