Can I have my son's school pay for his medical expenses due to their NEGLIGENCE?

During Lunch recess, my 8 year old son fell from the Monkey bars at his School, and badly broke his arm. My son cried and held his arm and that clearly shows that his arm is hurt. And I do understand that kids do get hurt while at play. However, the situation was handled very poorly. The first teacher who seen him, physically moved his arm up and down while asking him, "Can you move your arm?" while he is crying, he's telling her "YES!" and we do have witnesses of her moving his broken arm while in pain (No School Nurse was notified nor parents) He then notifies his Home Room teacher that his arm hurts from falling from the Monkey Bars, STILL no procedures were followed. The HR teacher tells him to get an ICE PACK from the office (Teacher did not look at arm). My son goes to the Office for an Ice pack and was given one, but STILL no one noticed his broken arm. The person who gave him the ice pack did not ask him why? Or even bothered to ask. He got his Ice Pack and went back to class (STILL parents are NOT notified or School Nurse) He returns to class. He tries to write but then tell's his teacher his arm hurts when he writes. Teacher states, "just keep the ICE PACK on it". My poor son sat in class in pain with a broken arm all the way till he got home from the bus and that was 4:20pm. We still were not notified of any accident. We noticed his arm at home and took him to the ER. It was visible and clear that his arm was not right. The X-ray showed his bone is broken. They referred us to a bone specialist. Now we need to look for a Surgeon. He needs pins in his arm. His arm will never be the same and I BLAME the school for their negligence, poor first aid knowledge, and no procedures and follow-ups. They showed no concern of the well-being of my son, no apology, no Sympathy from the teachers or Principal. The principal is more concern of an accident report that they are trying to put together the day after the accident.