What happens if you’re sick when you have the baby?

We have a 2 year old who was getting sick constantly from preschool. I took him out last month permanently because of it. I work from home with him and have been a total freak the last few weeks trying to keep him (and my husband and I) healthy for whenever baby arrives. For various reasons I likely won’t be making it to my due date of Jan 13th and today my son woke up with a runny nose and congestion. If I catch whatever he has what will happen if I go into labor??? I’m so upset about it.