A.K.
I had this problem with my step daughter, I tricked her. I would cut up broccoli cut it up small cover it in cheese and she ate it, after she did I said to her "Wasnt that good broccoli?" she had no idea. I did the same thing when we went to chinese food one day and she loved it slowly after that I would do things like take some carrots and ranch and eat it as a snack and she slowly tried each thing, it was a slow process. Now I cant keep them in the fridge.
Her favorite food is now chinese food!
The more of a reaction she gets from making herself gag and not eating it she will continue to do it. When she sees that you wont get upset anymore then she will find a new way to get a reaction from you!
Good Luck! ~A.