Oh hey, I know I already gave you my opinion but I just thought of this. Why don't you ask your doctor to refer you to a dietician as well as a shrink? That way your parents and your doctor can be assured that you're eating a healthy diet.
I went totally vegan while in recovery for my ED and something that made my nutritionist and parents more willing to let me go through with it was eating vegan replacements for dairy foods. For example, we all know that calcium can be found in leafy greens, lentils etc. but just to show everyone that you're eating enough and healthfully the may feel better seeing you eat soy yogurt or (not light) soy milk. If something looks like a glass of milk, omnis become more at ease sometimes.
if you accept to eat a little dairy, they will respect that you are mature enough to want to do it for your health...suggest you only want to have organic milk or yoghurt you should be able to source these from health store...better yet prove to them that alternative products can contain calcium, protein etc if that is what they r worried about...soon enough you can make choices for the rest of your life
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