My kitten was thrown hard. What signs of injury should I check for?

I'm sorry to hear about the ordeal you and your kitten have been through. I would check your kitten over for any obvious injuries first, such as severe fractures or obvious bleeding. I would make sure that it is walking properly and does not appear to be having any issues with balance or equilibrium. If none of these seem to be a problem, going to the vet right away might not be necessary. If over the next 24 hours, you start to see any issues that may be attributable to pain or shock, have your kitten checked out by your veterinarian. Lastly, make sure that your dad has no more access to your cat since he clearly doesn't know how to handle one properly. If this means finding it a new home, it may be in its best interest.