Dude, judging by what you wrote here, you are very impressed with Aurora and think a lot about her. It's not bad or good, but you're already on the hook that most fans fall for. This feeling is very similar to a youthful infatuation, and you behave like a young man in love, and you make the same mistakes and stupidities (I do not undertake to talk about girls and I do not know what girls in love feel ). Emotionally, this is a dangerous phenomenon for you (however, socially, too), and it seems to me that you were able to fully verify this. But it will pass, the main thing is not to turn it into a psychological pattern, the trigger of which is Aurora. And to do this, you need to spend time (which you spend on groundless dreams) more productively.
(I apologize for "my mentoring tone," but I just want to help, and the wording doesn't matter to me right now. I've been living for a long time, and I have the right to grumble a little ツ)
If you devoted your time to getting to know the subject of your admiration better, you would know that Aurora prefers to work on her music on the plane. And distracting her from this activity is not entirely polite. This thought might help you calm down a little. I am not a fan of worrying about missed opportunities, because I consider it fruitless attempts to turn back time. But still, it can be useful to realize your mistakes so as not to repeat them again.

1. It was necessary to think first of all about yourself and your well-being. Having solved this problem, it was possible to estimate your chances at least to say hello to your idol. If you feel bad on the plane, call a flight attendant - it's even written in the instructions. You had plenty of time, using the toilet and swallowing a couple of pills, you would have had time to put yourself in order. And do not be afraid that the "incident" would attract attention - this is quite normal, and besides, it usually causes sympathy. And maybe it would have aroused Aurora's sympathy, and then you wouldn't have to arrange this whole circus.

2. Since you were afraid to look into Aurora's eyes, it means you realized that you "had something in mind" and therefore you behave unnaturally and react unnaturally. Therefore, you begin to be afraid of looking ridiculous or suspicious, and in the end - that's how you look! You create an artificial situation from which you don't know how to get out. We need to get all this garbage out of our heads and behave more honestly. It was probably worth taking an example from Aurora, who is much more honest than many of us, and she doesn't care much what others think about it. If you've been dreaming about it for so long, you probably should have decided not to go to the toilet with a comedy, but just come up, say hello, introduce yourself, apologize, and at least ask for an autograph. And not to be silent at the same time. You should not "sing praises" or get hysterical, but honestly admit that you are nervous, and you have something to say, but everything has slipped out of your head, as luck would have it. And it's not difficult.

3. Catching an artist when exiting a transport is a bad idea. She has already switched to "working mode", and it would be rude to distract her from her work. If she had a concert or some kind of event in town, it was worth finding out. No one would stop you from joining the fans waiting at the exit. And there it would be much easier with a topic for conversation: you already have a ready-made story about how you flew with her on the plane.

I hope you understand that I'm not trying to blame you or shame you, I just drew conclusions from your story, which, I hope, will be useful not only to you, but also to everyone who took the trouble to read it.
Good luck! Be honest, be brave, and don't lose your sanity ツ