Is Buddhism about being less "sensitive"?

I'm just curious, since before I began practicing the Buddhist way of life, I was a very emotionally sensitive person. I constantly had my "feelings hurt" or got into petty arguments over small things in life with people who were once my friends. Sometimes this broke apart many friendships. However, a lot of Buddhist teachings seem to deal with detatchment from the ego, therefore as to loosen or weaken one's sense of self. I found that sometimes I no longer clung to my opinion about reality as if it was absolutely right. But what about emotions? Is Buddhism about taming one's emotions (I grew up as an often very emotional individual on many ends of the spectrum)? Or does one approach emotions by letting them manifest opnely? In short, in my practice, how can I go about dealing with my innate sensitivity? Thank you.