If your baby has been stung on the face, it is recommended to apply a cold compress to reduce swelling. You can use a towel soaked in cold water or ice wrapped in a towel for 10-15 minutes at a time as needed throughout the day. It is better to avoid using Benadryl unless there is a widespread reaction on the body, as it can cause drowsiness or excitability, especially in young children. Be cautious with the dosage if you do decide to use Benadryl, as it should be based on your child's weight. Always consult a healthcare professional for advice on medication dosages and usage.