Is it normal to have a desire to explain how someone hurt you

I was wondering if this is normal because maybe most people do this already but I am a very closed lipped person. I dont share how I feel. If someone hurts me I confront them about it and im quite angry. I ask them why but I never say how I feel about it. I dont cry or say "I feel hurt", but I throw questions like "why did you do this?" and say "this is not okay and I will not tolerate it". Most people says im cold and that when I get upset it is scary apparently. Not sure why since I stay calm I dont even raise my voice. I dont think ive ever raised my voice at anyone.... I just sit the person im mad at down, stare at them and ask them about what they did calmly. I think its a good technique though because people have told me the way I communicate makes it feel they cant lie to me.
Anyway I always when the anger has rinsed off me daydream about meeting the person by chance and taking the opportunity to confront them. To ask them the specific questions I never asked and to pour my heart out. To tell them exactly how I see them, that they hurt me, how much I cared about them and how everything made me feel. To see them experience guilt and shame while unloading every feeling like people do in movies. In some cases maybe the person would only care on the surface if at all but in some cases maybe they would realize something and feel bad. I always wonder what difference not holding back emotions could make. I feel sometimes like even people who was really interested in me and not just playing games moves on easily because I didnt show them how I felt and like I have to carry all emotions by myself all the time good and bad.