Different people, different reactions

Today I proved once more that I can act coldly when something bad happens and my help is needed, but the moment I check everything is OK, I tend to relax and feel anguish.
One of my friends fell my school's stairs, and it's not that she just missed one or two steps...she rolled all the way down to the bottom floor. I was at the bathroom at that moment and I was shocked when I listened to a hard sound as if someone had hammered a wall.
I hurried myself to go out and check where this sound came. While I was hurrying, I heard someone saying "someone fell the stairs", and I worried even more. When I managed to go out and see downstairs, there was my friend in shock. I rushed to her side asking if she was OK but I couldn't receive an answer. I asked again and since I couldn't get a word from her, I left her sitting there and run to look for someone to help me.
When we went back, she managed to walk up to the staff room and we waited there for the ambulance to come.
Luckily, nothing happened to her, but we were all worried.
And I began saying "I proved myself once more" because whenever my mother or my younger brother are around me, and someone in the family gets hurt...they block their minds and start coming and going, but actually doing nothing (I call them rubber knives).
I'll give an examples so as to help when drawing a picture of them. When my son was 4, he was playing in my mother's house and running to catch her dog, at some point, he slipped and hit his head with a door's threshold, cutting her head. When we heard him crying, we went to see if he was OK and found out that her head was bleeding a lot. I instantly tried to cover the wound with my hand but my mother started crying. I said "Mum, calm down because you are not helping and call a taxi", she ran to the phone and got angry with the women who got her call, because there where no taxis available. Then I said "Mum, give me the phone so as to call my husband, and calm down". She never waited me to call my husband and went out to ask a neighbour to drive us to a CAPS which is near her house.
When we got there, my mother entered screaming for help, and I was making jokes to my son asking him not to pay attention to my mother. In the end a nurse helped us and made a comment about my son's and my easiness and laughed about my mother's anxiety. Of course, when I went back to my house, and after checking that no one was seeing me, I started crying because my obvious mother's fear wanted to come out.
My brother, on the other hand, was in shock when his best friend broke his arm, and went back home without accompanying him to the hospital. When he got there, I told him, "Let's go and see if he is OK. Maybe he needs something and is alone... Why on earth you're not with him by now?". He couldn't manage to move a muscle to say anything, and with his eyes struggling with guilt, after a while he answered: "OK, are you coming or not?". When we got to the hospital, we looked for my brother's friend and the doctors where trying to line his bones again, so as to put him a huge cast which covered part of his chest and his left arm. My brother was mute. He wouldn't say even a word. I said: "Martin, don't worry, we've already called your father, my brother is here and I'll talk with the receptionist about the papers that you have to fill in. Don't worry". After an hour or so, my brother started talking again.
The thing is, that I don't really know if I'm like that because of my mother's influence (whenever I got hurt she would tell me off), or is it just a difference in some people's character, the thing is that I leave the nervous breakdown for the moment in which I'm certain that everything is OK.