Have you had regular pediatric check-ups? This really sounds like an issue for your parents to take up with your doctor.
If you google "toe walking" you can get a lot of your answers, but it seems like your parents need to be involved in seeking help for you.
It also may be that something as simple as orthopedic arches which you wear in your shoes could solve your problem. Since I think that this is more than just a "foot" problem, I would go see an orthopedic doctor. A foot doctor could tell you if arch supports are needed. A less costly experiment would be to go to a running store that can analyze your footfall pattern (I know that roadrunner does this - there may be others), and then buy the shoe they recommend based on your footfall pattern (they have machines that do this). See if this makes a difference.
But it does sound like you have very tight Achilles tendons. Given that, I would go see a orthopedic specialist. They should be able to tell you what to do.