My son has the same problem; he gets stressed and panicked when we fly because of a sense of being closed in a small space. What works WONDERS for him is taking Drammamine; even though it is an air-sickness remedy, it just kind of creates a calm feeling for him -- taking it allows him to sleep (and we are also about a 2 hour flight away from WDW). He takes one tablet about 30 minutes before take-off, and he's fine (not drowsy) when we get there.
If you want to try this, I would recommend finding a time to take it before you go, just to see what it feels like and to find out how sleepy it makes you feel (so that you can adjust your dose and take 1/2 a tablet, if nec., so you are alert when you arrive).
Do NOT ride Mission Space, btw -- it is a very small, tight, enclosed space.