I used to be like this too. And in real emergencies I still am. Hey someone has to keep their head on straight and take care of every one else.
Delayed reactions are normal. Can I stress that again? NORMAL.
The trick, however, is to realize what the reaction is and actually allow yourself the time to experience those feelings. Ignoring them or telling yourself that the feelings means there is something wrong with you is counter-productive and often leads to stress-related illnesses. Burying them will be more harmful in the end that acknowleding them and expressing them in a healthy way.
My delay reaction used to be about two weeks after the event. It made it almost impossible to remember what triggered them. But once I realized what they were connected to, I was able to train myself to think about how I felt shortly after the incident. I slowly was able to get myself down to a couple of days later, then a couple of hours. Now I can acknowledge them during, but I can also say, I can't deal with the emotions right now but I WILL do it later, and then make time to sort through those feelings.