Quite a lot of people are uncomfortable with me too Silver, but then I'm not human, except in the most unimportant and superficial way of course, so that explains it for me.
If you feel like you might be different, then there is a better than average chance that you're only superficially human too. (humans are very rarely different, and rarely make each other uncomfortable!)
The bits of your post that shout loudest to me are
1. You have spoken to your friend about it and asked her counsel.
2. She has given you her best advice, and you trust her and her judgement, and yet you still don't want to take it.
3. You have thought about it and feel that you simply can't just walk away and forget about it.
4. You feel that something is 'missing'.
5. You have always wanted to fly and feel the wind in your hair. So much that you have even had dreams about it.
Taken on their own none of these points means very much, but when you group them together like this it may mean something.
I think it would be a good idea to look into it. Even if you find nothing, because there might be nothing to find, then at least you will have looked, and you can move on knowing that you tried. You didn't just say of course I couldn't be something else, I'm human and that's that.
No matter what you feel you may or may not be, if you
settle for anything it would be a mistake. Whatever you do in your life, even for a career/job, you should never settle.
Always aim for the highest you can get, and always aim to be yourself no matter what.

Whisper's post is a great place to start. Even if all you ever see is a human reflection, it won't be a waste of time, and you won't hurt yourself or anyone else by looking into it.

Good luck.
Faith