Yes! Yes, many people w/asthma fly and fly regularly. Just make sure you tell your family physician about your plans. It would be helpful if your asthma is under control. Have all your medications on hand, both prevention & rescue, especially the latter, god forbid you have an attack mid-air. Make sure you don't need extra oxygen as cabins are pressurized to anywhere from 4, 000-9, 000'.
Happy travels. Commercial airliners are pressurized to about 6000 foot elevation which is well tolerated by almost all asthmatics. Be sure you take your daily maintenance medications and have your saba reliever on your person. Relax and enjoy your trip. Anxiety is a much more likely otherwise to affect you breathing than the actual flight.