I don't know how much you have lurked on the board but transsexuals can be discovered from age 3 to past age 60. There is no set age you know when you are transsexual but it's pretty common to figure it out by the time puberty hits. While there is a 1 in 600 chance of being born transsexual, the fact you are on this board indicates you are the one.
As for fixing you, my mother figured she could fix me and found my first therapist. He was a nice guy but he knew he didn't have a clue how to treat me. He did find possible treatment in California where I moved to and eventually did receive proper treatment.
At least your parents are like mine in that they aren't attempting to kick you out and are trying to get you some form of therapy. I don't think any therapist will ever talk you out of what you feel but there are a few that will try, If you encounter one, explain to them that you know better and unless they will provide real treatment, you will refuse to cooperate.