I have this too. I have had it all my life and I used to cry whever I or someone was sick. Now I hate travelling on the plane, or on school trips on the coach in case someone gets motion sickness. I get very hot and shaky, and I sort of lose my wits, getting very anxious. I won't go near anyone when people are sick, even if they are trying to calm me down. I will run away and get away as soon as possible no matter what. I will act very coldly to the ill person and be sometimes quite snappy and mean, but I don't want to hurt their feelings really.
Its nice to know that I'm not the only one!