I thought my family would freak out, and they did somewhat, but I dealt with it and they eventually came around. I came out at 27. Just don't do what I did: go hide from yourself and your parents, and get involved in drugs. Yea, it taught me a lot but I'm rather lucky to be alive (the whole selfish point was to eventually die and oh cruel world...OMG as if that'd have been easier on my parents!).
If your dysphoria is THIS bad, then one day you most likely come out, and it won't be easy.
Now this is ONLY MYSELF, but gosh if i were your age knowing what I know now I'd lightly break it to them in some hintish manner. If they refuse to acknowledge it, then I'd flat tell them the truth, and that there is nothing they can do to change who i am! That'd sure have saved them a lot of legal fees, hospital bills, worries and gosh so many tears.
...but it almost had to be this way, or things would have been different, and they wouldn't have begged me to tell the truth about what was wrong that "one last time" when I actually told the truth for once, and thusly I came out!
I know you feel powerless hunny, but the best thing you can do TODAY is to get informed. FIND A LOCAL GROUP FOR SUPPORT AND FIGURE OUT A WAY TO GET THERE! GOOGLE THAT JUNK EH! Drive ther, or take train, or maybe even get a ride from your Mum or Dad as subtle way to break it to them. JUST GO!
Most GOOD parents may think their child is being selfish at first, but then in time they realise no, it is they who are behaving selfishly in not allowing their child to live out his/her dreams (not THEIR dreams as parents).
Oh it was tough, but today I have the best relationship with my parents of my life, and their doubt has turned into solid support . Our decisions are all we've got, so please make good ones!