This is me, to a T. My "turn around time" is getting shorter, but I suspect I will always have a little of this. The two things that have helped the most:
1) Make sure the other person knows that it takes you additional time to process emotional hurts and forgive and forget, even if your rational mind is ready to move on. You're not wrong to feel pain, but you would probably be wrong to act on it if you have already resolved the situation with the other person.
2) If you're not ready to accept an apology when it is offered, (as calmly as possible) explain to the other person that you're still upset and you will come to them when you are able to talk about it. It's important that you follow through on this though!
It also often takes me a while to discuss anything that has made me emotional, whether it was my fault, someone else's fault, or shared blame. Both my partners know that I will come to them when I am back to being a sane person if something needs to be discussed. They give me the time and space needed and wait patiently, because I always follow through and COME BACK.