Rosacea is the first thing that comes to mind. Although, if you have been coughing or vomiting, they could very well just been broken blood vessels which should disappear within a few days.
Since it is under childcare, the most likely situation is the chicken pox. Most children get it though some are vaccinated against it. The MMR vaccine rules out Measles, Mumphs and Rubella. The...
First, it is very hard to decide what a red mark is ,without seeing it in 3d, and really that means you must visit a GP. A long term red patch is a result of a scrape or bump, or a burn, a cold burn...