There is a form called FAA Asthma Worksheet. You can google it. Take this form to the doctor who is treating you for Asthma. Make sure you get a Pulmonary Function test and get the results. Take all that paperwork with you to your AME.
I have allergy induced Asthma and have a Dulera inhaler as well as Montelukast/Singulair for seasonal allergies.