I wouldn't say it ever goes away, but it can become manageable. Logically, you should be able to say, "This is a disorder, it is all in my head," but this isn't a logical condition.
The best way to help with it is to get outside your head. I recommend doing daily gratitude. It may seem like nothing, but it can make a HUGE difference. Even if you just write down three things you are grateful for every day it will start making a difference after 4 days of consistency. Also, try meditation. Headspace is a good place to start for that.
In addition, find ways to serve others. You can formally volunteer somewhere or just look for opportunities big and small around you to help other people. When you can see REAL problems that other people are dealing with it can help you put your own problems into perspective. For example, if you are volunteering at a hospital and work with someone in the burn unit who has had half of her face melted off in a fire you might realize that "weird eyelids" are very minor compared to that.
Also, remind yourself that being different isn't necessarily worse. This may sound weird at the moment, but perhaps a future boyfriend or even husband may fall in love with you partly because of your unique eyelids. What you find weird may be exotic and special to him.
Finally, the best way to deal with anxiety is to face it and desensitize yourself to it, not to hide from it. I'm not talking about going crazy. Challenge yourself to the point that you feel challenged and out of your comfort zone, but not to the point that you are overwhelmed and are going to completely break down. This may mean challenging yourself to go out in public one extra time each week. Or maybe it means talking to a stranger each week. Or maybe it means going to the store each week without any makeup. What sounds scary to you but is something you know you can do? Go and do that. You can't make your anxiety go away, but you can fight back and stop it from controlling you.
Know that no matter how weird or ugly you are, (assuming you even are weird or ugly, which I doubt), it won't matter to anyone who SHOULD be in your life in any meaningful way. If your best friend or mother or daughter was in a horrible accident and majorly disfigured her face to the point that she didn't look human anymore would you stop loving her? Would you tell her that she'd better not go out in public because she is ugly and it isn't fair to the public to have to see her? Would you tell her she doesn't deserve to be loved or have a job or have friends or be in a romantic relationship just because the right side of her face looks like it has been through a meat grinder? My guess is that you wouldn't say any of these things. You would love that person and stand by her. If people in public were rude to her, you would tell them off and would continue to stand by her. You wouldn't tell her to give up on life and stop participating in public just because of something that shouldn't matter. Yes, there are people who would be jerks, but at the end of the day those people aren't important. If having your entire face horribly disfigured isn't a sufficient reason to stay home, then having unique eyelids that most people probably don't even notice and that are probably not even that bad certainly isn't. If you look at everyone's face without makeup, there isn't a single human being out there that doesn't have some very weird feature. Maybe even make it a game to notice other people's weird features. But most of us ignore each other's weird features most of the time. Maybe one person has a funny shape to her nose. Another has an oddly shaped chin. Yet another woman has an annoying and ugly black hair that grows out of her cheek that she is constantly having to shave. Another woman deals constantly with the abnormally long nose hairs. Some when have to shave hair out of their ears. Other women have scars left over from when they were teenagers and couldn't leave their acne alone. Some women hate their freckles, while others hate the fact that they don't have any freckles. There is no such thing as a publicly presentable face. We just have to suck it up and publicly present our faces even though they aren't fit for public presentation because if we didn't no one would be allowed out of the house ever.
Edit: Something else I forgot to mention is to try paradoxical intention. This is a strategy where you intentionally try to do the thing that scares you. It helps best if you can be truly ridiculous and laugh. It can also start with a lie. So for example, tomorrow if you go to the store you tell yourself, "Yesterday, I scared 2 men out of the store with my crazy eyelids. Today I can at a minimum scare 3 men and 3 women out of the store. They will be screaming so loud about my crazy eyelids that everyone in the entire store will hear them." Then go out and actually try to scare people with your eyelids. If you are afraid of your anxiety about your eyelids, you can also add, "After I scare those 3 men and 3 women out of the store I will show them that I have the worst anxiety of anyone in the whole world. I am going to force my heart to beat out of my chest, and then I will pass out from my anxiety. I bet I can even die from embarrassment."