When I was a young adult, I was the opposite. I made myself turn hard like a rock, was numb and didn't feel much at all. I don't think that was healthy either. -- When children find it necessary to adopt a coping mechanism to deal with a situation, it is healthy, because it protects them and their minds from overwhelming things. It is a survival tool. If that mechanism continues to be employed into adulthood, it is unhealthy. It's called dissociation.

Usually, however, the coping mechanism morphs into another form of dissociation in adulthood if the root causes for the original dissociation have not been addressed. In your case, I'd say though that your coping mechanism is or has been breaking down and causing you to be flooded by emotion, especially, anger.

It is important for you to acknowledge emotions as they arise and identify them quickly. If it is overwhelming or becoming overwhelming, there is nothing wrong with diffusing it and creating a little space for yourself in order to come back to the issue and deal with it calmly. You can do this by saying something like "I want to address and resolve this with you but am becoming angry (emotional) about it right now. Can we talk about this in an hour (or whatever time you think you may need). Say this as calmly as you can so that the other person can see that you are serious about wanting to resolve it and not side-stepping the issue. It will take some practice and be patient with yourself.

Your feelings are your feelings. You cannot "control" the feelings you have or get, but you can control what you do with them. That's the key. Not pushing down emotions or allowing them to get out of control. Identify, acknowledge and accept the feelings.