Breaking up does hurt. You just have to accept it and understand that it dissipates with time, no matter how it may feel right now. Actually, I suggest embracing the pain and hurt and emptiness you feel right now. Allow yourself to cry. Allow yourself to wallow. Be miserable for a little while. You will bounce back from it. And it will give you a better understanding to the depths of your emotions.
It sounds like you broke up because of logical reasons. That will help you in the long term get over things. But emotions don't follow logic. Your heart is hurting even though your mind knows it was right. That is why I suggest allowing your heeart to have its moment here. Your mind is going to guide you forward, but you don't want to become a machine. You need that balance in life.
It is important to remember good times. And you can ease yourself a little by realizing that the person you are now and the person you will be going forward has been shaped by this relationship. Allow that to provide some comfort to you, because in a way, you will be who you are because of her and she because of you.
Good luck.