Ditto what DeeDee said.
Building healthy coping skills is very, very key to fostering resilience in the face of what life throws at pretty much everyone. Those who are more sensitive probably need even more robust and varied methods of coping well.
We found that using the Jane Goodall approach worked very well in literature and film selections-- that is, in fiction, DD (even at 3-5yo) had the necessary distance to analytically evaluate the humanoids as they interacted and resolved conflict. She could speculate about their motivations and emotions behind statements and actions, etc. (Yes, the Spock voice is intentional there-- this is actually a VERY effective tool for gifted children, I think.)
This also played to her empathetic strengths, in that it allowed her to see that even "scary" human behaviors often serve a purpose in the person exhibiting them. That is, they are still human beings, reacting in very human ways.
She was eventually able to leverage that understanding and empathy for truly formidable coping skills and social awareness.
Social anxiety is not a huge problem for her-- and she is definitely hard wired for major anxiety otherwise. So I think that this method was highly successful for her. Individual results will vary, though, I expect-- kids are really individualistic.
My suggestion is to leverage strengths to help develop that insight and with it, better coping skills. DD retreats into "analytical" mode to cope with emotionally overwhelming circumstances, which is a fairly adaptive method under most conditions.
