Calm down. If you are freaking out, your child will freak out.
First, run it under cold water. Let the water keep running over it for several minutes. DO NOT USE ICE WATER as this can further damage the skin.
Next, gently dry it off and have a look at it. Edit your message and tell us how big it is, where it is, is it blistered, is it open or oozing, and any other details you can give. I can tell you what is needed with that information. DO NOT PUT ANY KIND OF GREASE OR NEOSPORIN ON THE BURN UNTIL IT IS FULLY ASSESSED. If you have an open (3rd degree) burn you need to seek professional medical attention. If you do have an open wound, use sterile gauze soaked in water or a peice of saran wrap to cover the wound on the trip to the ER.
If it is very large, say covering the whole finger or more, CALMLY pack up a bag with the baby necessities, call your pediatrician and see if they suggest that you take your baby to the ER