Should I still go to work if I have been exposed to scarlet fever?

If no fever. If you feel fine (no sore throat) and you have no fever then you may go to work. Scarlet fever is just a bad case of strep throat with a rash.
No reason not to. You are exposed to strep every day.There are asymptomatic carriers among any group of 20 people you have contact with on every given day. Scarlet fever is nothing more than just strep with a label that dates back before antibiotics. If you are not sick, no problem.