Is anyone so sensitive that they appear apathetic to others?

I don't know if anyone is like this, but I'm so ultra sensitive that I do not want to have friends and this appears to others that I don't care about anybody. The reason I don't want friends is because I know I'll avoid them when they start talking about hard times in their lives and feelings of sadness. This is not because I don't care about them and I don't want to help them, but because this will make me so affected that their own misfortunes would attach themselves to me and I'll probably feel even worse than them; of course avoiding them at these times would make me look cold-hearted. In reality, I love helping and donating to people at the impersonal level. Also, whenever I'm watching a sad movie with someone, I can feel myself about to cry as my shoulders start to shake when I try to hold it in. Sometimes when I do this, I need to laugh to relieve myself because I know if I let tears come down, they won't stop. If a third party would observe this, it'll look like I'm laughing at the sad situation in the movie. To make my sensitivity even more apparent, I sometimes feel like weeping when I peruse online debating boards and I see people call each other names and be cruel to each other. When I refuse to partake in these kind of conversations, I suppose it'll seem like I couldn't care less, but really, I would be running away in fear of getting hurt myself while viewing others being verbally abused. To top it of, I'm struggling months later to forgive my friend for declaring ending his friendship with me because I didn't stay online to help him with something. He said he still loves me as a friend and we're past that, but now whenever I talk to him I think of him demonstrating his ability to just drop me like I'm nothing to him and it still hurts. I hate to say this, but I don't think I like him as much as I did before this happened.