You are asking a very good question. Feelings are not negative or positive. They are an important source of information. They tell us when something or someone we love is threatened. They tell us when something is important or tender or frightening. For that reason, I don’t think there is such a thing as being “too sensitive.” I think your problem isn’t your feelings. It’s knowing how to read them and how to manage them.
Most men have had little teaching or experience in managing their feelings. Often men hold back their feelings so much that when they do let them out, they come out in a flood. They turn their emotional pain into anger because that is somehow seen as “more manly.” As you are finding, it is not a satisfactory solution.
If we were working together, I’d want to learn more about what triggers the floods of emotion and whether there might be a way to help you resolve them or manage them differently. I would also explore with you what would happen if you gave yourself permission to let out your feelings a little bit all the time instead of trying to shut them down most of the time. In addition, we would practice some new skills for coping with the things that offend you.
I encourage you to find a counselor who could help you learn the skills you need to feel more confident in your ability to use your feelings well. Please don’t pack them away. The world needs more sensitive men.
I wish you well.