I have GAD (generalized anxiety disorder) as well, and I have also flown by myself. I won't lie, I don't like it one bit, but you can get through it. The only airports I ever had any trouble in were JFK and the one in Paris, but that's because they're about 10 times bigger than they have any right to be, and many of the employees don't speak English very well. Just make sure you know exactly what gate is yours and what time your flight leaves!
Also, I've only had my luggage lost once out of five overseas trips, and it was found within a couple of days (I love the Germans!
). However, for peace of mind and just on the in-case, bring clothes and definitely some clean underwear and your essentials (medicine, toothbrush, etc.) in your carry-on. Good luck!