I just created my new character 2 hours ago and I've reached a town. Sometimes random guards will comment that I look ill, or that I should rest. "You look sick, honey. Do you want to lie down?", isn't uncommon.
Did I unexpectedly get vampirism? I didn't fight any vampires, only a couple of wolves and bandits.
I'm a dark elf, so maybe my race isn't seen much around Skyrim and the remarks are more roleplay than actual illness.