Honestly, all 4 of us are very sensitive. My daughter is the most sensitive, at least right now. She totally reminds me of myself when I was a child. I feel like she's being introduced to much better coping skills than I ever had.
I wouldn't be surprised if there was a strong correlation between being GT and depression (or anxiety, OCD, etc). Actually, this is part of the reason I feel so strongly about finding an educational fit that works for my kids. I was at least somewhat depressed my entire elementary school career. It's about being happy and finding peers and positive outlets to enjoy.