I actually have had similar experience, but not necessarily with flying. It was reffing basketball. I am a contact lens wearer, but I got an eye irritation and couldn't wear my contacts. So I had to wear my glasses when reffing the basketball game and it was so difficult. I couldn't see anything out of my peripheral and there were times when I just couldn't see what I needed to. So I understand to a degree the frustration you are feeling.
Don't let being worried about touching your eye stop you from trying contacts. I promise you'll be able to overcome it and after a few weeks you'll wonder how you ever struggled in the beginning.
Also, as previously mentioned there is so many new developments in the world of contact lenses that even if your eyes are dry like mine, there are special contacts to help keep in moisture. But it is true that my eyes get dry on planes, and when your eye gets dry the eye gets a little irritated, but I am only wearing the Acuvue 2, not like the
Acvue Oasys or other contacts specially designed for dry eyes.
Some people who have astigmatism do see better with glasses than with contacts, but then again, their are contacts designed specifically for astigmatism (toric lenses). But it just depends on you.
If one of your contacts happens to pop out while you are flying you can just pop out the other one (as you practice taking them in and out you'll get the hang of taking them out quickly) and put on your glasses, or you can just fly with only one in for a short time until you can take care of it.
Advice: always carry your glasses, contact solution, and a contact case with you wherever you go and have them handy. You never know when you'll need it.