Babies can get rashes on their face when teething although the rash doesn't actually happen as a direct result of the teething.
The babies rash on their face when teething happens because of the saliva also known as drool that comes into contact with the babies delicate and sensitive skin.
If the drool or Saliva is not washed off the babies face often enough then the drool can cause a rash on the babies face during teething.
So if your baby is teething be sure to use a damp washcloth or baby wipes to clean your babies face often when they're drooling during teething or any other time they may be drooling.