Swine flu vaccine concerns with worried teen?

I'm a 16 year old girl with muscular dystrophy. I was told by my pediatrician and pulmonologist quite vehemently to get the swine flu injection as soon as I could because of my vulnerability. I have a prescription of Tamiflu, but I'm still worried. There haven't been many outbreaks at all where I live, but now my parents are weary of the vaccine since all of these ridiculous rumors have gone around. I want the vaccine - just to be safe - but my parents are doubting whether I should or should not get the injection. I'm going to see if I can call my doctor and let her convince them but before I do that, what can I tell them to ease their minds?