Too Sensitive

What do you do with a kid who is just too sensitive? Shauna just came running in, screaming and threw herself on the couch, sobbing. It turns out that she, Hannah, Alex and their friend, Shannon were on the front porch and Alex said, "Shauna doesn't drink milk or water, cool people drink milk and water." Okay, so not the nicest thing to say, but bad enough for a huge fit of temper?

She has always been like this, but now at age 10, it is getting worse. I don't know what to do. How can I convince her that she needs to lighten up? I tried to explain to her about "growing a thicker skin" and she just screeched and refused to listen. Ugh!