Sarah-
No competent therapist will try to make you beat this phobia through vomitting yourself. There is something called exposure therapy, which involves looking at cartoons, pictures, and videos- but this is done gradually, and you move at the level you are comfortable with. It definitely does not involve you vomitting yourself!
I say definitely look into your options in regards to therapy- you are so young! There is a good chance that if you get help now you don't have to be like this for the rest of your life. A word of caution though- it may take going to a few therapists before you find one that you feel comfortable working with, or that is competent in treating this phobia (or the other issues surrounding it- often it is tied to something else that is completely not related).
As for your parents- although it may feel as though they are frustrated with you, a lot of it probably has to do with their own frustrations regarding their helplessness. It can't be easy seeing your child suffer and not be able to remedy the situation yourself. There are a lot of resources on this site- maybe some will be helpful to print out and show to them?
Good Luck,
*amber*
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