Hi Dave Tyler.
Postings in this thread offer you good suggestions. Counselling may be useful.
Emotionally sensitive people tend to feel things sooner than others, and yet, they may be very good at denial or repressing emotions. If a person doesn't seem to sense emotion, that person may have numbed himself from painful feelings or may have never learned emotional awareness. Sensitive people I have known were influenced by abusive environments. They learned ways to numb themselves from their feelings because so many of their feelings are painful.
I would recommend Daniel Coleman's book called
Emotional Intelligence Barnes***&***Noble.com - Books: Emotional Intelligence, by Daniel P. Goleman, Hardcover, 10th Anniversary edition