I've just started playing Skyrim and I've noticed that everyone is asking me whether I'm sick. I don't get this. Is this something connected to the skin color I have?
Maybe you have a disease I think. Check Active Effects.– JimOct 11, 2015 at 18:06
You simply have a disease at the moment.
In Skyrim, you can contract diseases. NPCs often tell you things about or ask about traits that you currently have, and diseases are one of those.
To see if you currently have any diseases, and if so which ones, open your magic menu. There will be a category called "active effects". The effects shown in red will be negative, and in some cases diseases.