Ask your doctor for valium (or similar) before your next flight. Something like valium will help remove the anxiety of the flight and perhaps even allow you to sleep for part of it. If you can teach your primal brain that everything is ok again you'll likely lose the fear as quickly as you gained it.
You just needs some experiences without the anxiety to help your subconscious learn that fear is not a useful reaction to flying.
Simply breaking the fear cycle sounds like the key for you since you learned the fear recently rather than had it from some buried childhood experience.
Another good thing to try if you don't want meds is to accept the anxiety rather than overcome it. While panic comes on observe what it feels like, let it wash over you, acquiesce to it. This has worked for me in the past with panic attacks, it is quite effective if you can get yourself into enough presence to try it. You'll find that underneath the panic or anxiety is nothing, do some belly deep breathing to help, and maybe learn a bit of light meditation to take yourself deeper. But seriously, beating anxiety in general is more about allowing it than rejecting it.
You just needs some experiences without the anxiety to help your subconscious learn that fear is not a useful reaction to flying.
Simply breaking the fear cycle sounds like the key for you since you learned the fear recently rather than had it from some buried childhood experience.
Another good thing to try if you don't want meds is to accept the anxiety rather than overcome it. While panic comes on observe what it feels like, let it wash over you, acquiesce to it. This has worked for me in the past with panic attacks, it is quite effective if you can get yourself into enough presence to try it. You'll find that underneath the panic or anxiety is nothing, do some belly deep breathing to help, and maybe learn a bit of light meditation to take yourself deeper. But seriously, beating anxiety in general is more about allowing it than rejecting it.