How do you know if your ankle is sprained or broken?

I'd say its most likely broken if you can't bear weight. You should really get an x-ray to be sure. But as you said your dad won't take you to the doc so for the time being you can RICE it: Rest Ice Compress and Elevate. If your ankle doesn't improve then you definitely need to see a doc! You should really try and convince your dad to take you to the doc though because if it is broken, the sooner you get it treated the sooner it will get better.