I know it's really difficult but you just have to try and think, this won't hurt me. The chances of a plane crash is one in 10 million - and you still have an 80% survival rate!! Once you're on the plane, if you feel a little bit iffy, you can take a walk around the plane and most air hosts/hostesses will calm you down if you don't feel well. I once fainted on the plane (so not fun) and they were really nice, sat me down at the back of the plane with water until they were sure I was ok. Take an ipod/some music and a book/magazine you can take your mind off things with.
Anyway about the relaxing thing, as well as the breathing exercises, meditation really helps too - just sit and listen to relaxing music (I have a playlist if you want it), and even if you only have a few minutes I'd suggest
http://thequietplaceproject.com/ it's so relaxing.