Comforting Others

I am not a traditionally "supportive" person.
I do not enjoy highly emotional situations because I simply do not know how to react.  I feel uncomfortable.  I forget how to behave "appropriately."  I start shaking, stimming, flapping my arms, and shaking my hands.  My vocal cadence changes dramatically.  I speak in short, concise sentences with repeated, multisyllabic words.
When my friends are having difficult days, it is really hard for me to "be there" for them.  I really just don't know many ways to comfort adults, and my attempts are often clumsy, because I don't particularly want to be the person who is relied upon to comfort someone I love.
It's not that I don't love them or want them to feel better, it's just that I don't handle sad situations well.  When people are upset, I get upset.  And whenever I get uncomfortable, I find it really difficult to manage independently, let alone socially.
It's hard for me to comfort others.  I feel bad about that.  I wish I could be a "better" friend when it comes to comforting those in need.