Just simply tell your supervisor that you are scared of flying and you don't fly for this reason. Most people are sympathetic and will understand.
On a different note, let me offer a helpful suggestion. Of all the types of psychological problems, phobias are actually the easiest to cure. The best treatment for phobia is "exposure therapy". If you haven't already, seek out a "cognitive behavior therapist" and they will know what to do to help you.
Additionally, things like Valium and Xanax are excellent ways to help you deal with panic situations. In fact, the exposure therapy combined with Xanax is a very good way to help you learn to deal with panic, so that eventually over time you are retrained not to panic in those situations and you no longer need any medicine to help you get through it. In addition to a small dose of Xanax you can add a small dose of a beta-blocker. Beta-blockers prevent adrenaline. As the "adrenaline feedback loop" is one of the defining characteristics of a panic attack, the beta-blocker can help mitigate it as well.
If you end up using medication, you need to combine it with the cognitive behavior therapy because you don't want to get dependent on medication to deal with panic. Instead, your goal is to use the medication only as a temporary way of helping you analyze yourself and deal rationally with the panic situation, so that eventually you realize you don't actually need the medication.
If you want to talk more about this, message me privately, I'll be happy to discuss what I know.
Another thing to think about: a panic attack is a "fight or flight" response, which is your evolutionary response to protect yourself. Think about this. It's your body's own way of helping itself. Although, it happens to be misdirected at an inappropriate target (a plane, or whatever situation causes you to panic.) Everybody who has a panic attack thinks they're going to go crazy, pass out, die, etc., but it never happens. Nobody has died from a panic attack. How are you going to die from something that is actually your body's attempt to protect itself? You don't. What happens is you get into an adrenaline cycle: the adrenaline peaks, it tapers off, it peaks again 10-15 minutes later, tapers off again.... These are natural things designed to get you out of danger.