How do I tell her she hurts my feelings?

Sometimes us girls forget you guys have feelings too.
I know I have in the past. I have been guilty as the same thing as your friend in the past. The main thing is she most probably doesn't know what she is doing is hurting you - and if you don't in some way confront her about it - she'll not be any the wiser.
I suggest you wait for the next time someone says something along those lines and say something along the lines of "I'm not that bad am I?" or - if you fancy a lighter approach "well - the feeling's mutual."
Just something that highlights that you have taken notice to what she is saying. Once the topic is brought up - it should get a lot easier. Just tell her how you really feel - and that you'd appreciate her acting accordingly. Ask her to imagine being in your position - and how she'd feel; and suggest the other ways in which she could deal with it - like you said - her simply saying "we're not together" so that she will be sure that you're not trying to persuade her being with you wouldn't be so terrible so that she gets the wrong idea.
I'm sure she isn't happy that she's made you feel this way and will be happy enough to change her ways.

Wait.. you have never kissed a girl before? You're so pure, I wish there were more guys like you over here.
Anyways, I have a lot of guy friends, and we get teased just the same way. The only difference is, we both say "eeew" and make fun of each other ourselves, so its all fun. But in your case, if it hurts your feelings, the only thing you could do is talk to her. Like normal, and not too serious. Because that could get awkward.
Try bringing it up by saying something like "Its funny how a lot of people see us as brother/sister (that would be the most un-awkward example)", then see her reaction. If she shows the same disgusted reaction, then say "Is it that bad?" She will start explaining stuff... maybe even deny it. Then explain that you're just concerned about her, and if it embarrass her, then you'll quit being "too close" to her in public.
As a person with a lot of guy friends, If you said that to me, Id hear what you're REALLY trying to say, but if she doesn't get it, then tell her that she looks so offended when people tease you two, and you don't want that for her, and for you.
I suggest you don't mention that it hurts your feelings. I don't know what type of a person she is, but some women can get confused and hear it as, "I'm falling for you". And that might ruin your friendship. Try to act cool about it k? Good luck :)

Talk to her about it
ask her about those faces

I would ask her to put herself in your position and think of the impression and feeling she would get if she were in your position, and had the experience you had.

But being overly conscious about yourself is something to work on. Maybe you can bring that up, if she doesn't know your self conscious then maybe that's why she continues to do this. Maybe she can help you be not so self conscious if you talk to her about it.

I picture that when you're with her you're kind of outgoing, but when you're around other groups of friends you may be more inclined to be shy. But however, she wouldn't see this shy side of you if she isn't there when you hang out with the other friends or whatever, so she knows you to be more outgoing, at least around her.

Just these 3 magic words to her. well thanks asshole. tell her that she is a huge boost to your self esteem. be as sarcastic as possible, sometimes you gotta fight fire with fire. - just make sure you do finish this off by being truthful. and if she makes fun of you, tell her not to be angry that your friends with her because you want to bang her mom. -j