I am empathic to a fault, is there something wrong with me?

When I'm with someone, before they even start talking I instantly mold to their mood. I'm not exaggerating either, it's like I can sense what their mood is and I can't help but mimic it, even if I don't want to. I am very easily hurt, and people are rude to me because of it but I feel like I can't control it. I can mask it and pretend I'm not feeling anything but my emotions have a very physical role on my body. If I'm around someone who is very mad, I don't even have to hear them talk or have them be mad at me in order to feel physically angry. It's hard to explain but I feel like there's something very wrong with me. Empathy is supposed to be a good thing but it's like I'm so sensitive to people, I can't even control what I pick up on. Can other people do this? Why am I like this? I feel like there is something very wrong with me....