I had a similar experience two days ago: I was going to meet my study buddy and came upon an accident that had just happened. The driver (the husband of the woman passenger) stumbled out of the car, dazed, ankle hurting (but he could move it and there wasn't any evidence of bleeding or bones sticking out or anything) and saying over and over, "my wife, my wife." She was in the car, glass on her face and across her clothes, blood around her mouth and on her shirt, but nothing spirting or oozing. It looked like mouth trauma from maybe hitting the dashboard.
The car had hit a telephone pole straight on, and was sending out steam and a weird sick-car smell, but not gas so at least I didn't have to find out if I was brave! I crawled in, held her hand and tried to find a pulse (I think I was nervous--she had one, she was moaning and moving, but I couldn't find it). She was from India and there was someone who could speak her native language standing outside the passenger's side door talking to her, translating stuff I asked her to tell the woman like try not to move, help is coming, etc.
Finally, I heard sirens, so I said, I'm getting out now so the helpers can get in. And the woman turned her head just ever so slightly and held onto my hand and said in perfect English, please don't leave me.
You know I stayed until I was in the way.
You can't learn to be caring and to care, in school. That much, you already have--be ready to offer it when the need arises, and you will get the wonderful experience of really helping someone else.
What a life!