Well, it seems like preschool has only just begun and your child comes home with a cold or worse. No matter how much hand washing is done at home or at school, you can be sure that your preschooler with pick up a runny nose, sneeze, or cough before long.  
Obviously a really sick child is a worry and you will need to do whatever is necessary including doctor visits if called for, but here is what you need to know about the little viruses your preschooler will pick up – They are a necessary part of developing your child’s immune system. It would be strange if your child started school and did not catch some common viruses. “…, having lots of sniffles early in life may protect kids later on. Researchers have found that children who develop frequent colds in preschool catch fewer colds during their school years--presumably because their immune systems have learned to recognize and fight off the bugs. And a German study has found that babies who have more than one cold before their first birthday are less likely to develop asthma by age 7.”
That’s a quote from Parents.com’s aricle “35 Ways to Keep Your Kids Cold Free”
http://www.parents.com/health/cold-flu/cold/35-ways-to-keep-your-kids-cold-free/
The best advice is to follow basic health care; healthy food, fresh air, hand washing with soap and water, and plenty of rest. Teach children to cough or sneeze into their elbow not their hands, so they don’t automatically spread germs onto everything they touch. Lastly, don’t forget to take care of your own health by following the same guidelines. It’s not easy to get rest as a parent of little ones, but your health is more important than squeezing in the all the chores while your child naps!