Winter baby worries!!

Dacia
Anyone else terrified of their baby getting sick? My little one coughed today and I freaked out! I think he just choked on this saliva, but immediately I thought- whooping cough!!! 
  I had to take him out yesterday in the 20 degree weather to my  place of employment (childrens museum)  with lots of kids to turn in some paperwork and 2 of my coworkers who are grandmas held him. 
    I was happy to have them live on him but I was so uncomfortable the whole time. How do other mommas deal with the sickness anxiety??