Reddit reviews Basic Principles of Classical Ballet

The general opinion is that you cannot teach yourself ballet at home.

However you can show your parents that you are dedicated by reading books (i.e. Vaganovas Basic Principals of Classical Ballet, it's really not expensive and might also be available at you local library)

and do pilates excercises which will help you to get in shape. Depending on your age you can also try and find a job that allows you to pay for classes yourself.