Try to visualize something like that happening right now. NOW, stop and think to yourself... MY reaction is going to affect my child's reaction to this. No matter HOW bad it looks or how scary it is or how serious the long term repercussions might be to this injury... it will be WORSE if I send frightened signals to my child. Take a deep breath and just slow down.
Remind yourself that you MUST deal with the situation, and it can be hard or harder. The hard way you deal with it without getting hysterical. The harder way, you freak out and cause everyone to freak out in the process. Be the calm comfort your child needs. Imagine yourself as a nurse triaging your child at the ER... very matter of fact... "I know it hurts, but let mommy look at it." in a calm voice. Rinse with plain water under the faucet running slow (if it's feasible).... the sound of the water is distracting and soothing at the same time. And will give you a chance to think. Very few incidents around the home require immediate emergency care. Most need mom to comfort more than anything else in the first moments. You can DO that!! You're a pro at that! right? So do that. And give yourself a moment while you are doing that comforting to think of a logical course of action. Is it a cut?... rinse. Then decide if it might need stitches or just a band-aid. Is it a burn?.... cool running water is soothing. Or even a bowl of cool water, together with some tylenol. etc etc... comfort them and think what the priority of treatment might be.
I hope this helps.
I am the opposite. I go into almost complete disassociation/clinical mode. THEN, when I finally make a decision about getting ER treatment, I get really stressed about how to make the logistics work with everything else that is going on in the house (dinner, homework, picking up another child from activities, the dog, the playmate that is there, whether they'll be able to go to school tomorrow, etc etc etc).
Good luck. Not everyone is cut out to be a triage nurse. But you ARE cut out to be a great mommy, and that is the biggest part of accidental injury care at home. Be your child's "rock". :)