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.
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.