Kissing as an act of healing has a long history in the West, and the iconography of the kiss in general (sexual, greeting, healing, etc.) is complex -- but the instinct for wound licking (which humans exhibit just like other mammals) predates any recorded history. It's biological behavior. If you've ever cut your finger and instinctively put the injury in your mouth, that's an example of this instinct in action.

(More biology than history, but information about human wound licking and saliva's healing and antibiotic properties can be found in Nigel Benjamin's "Wound Licking and Nitric Oxide" paper or in this FASEB Journal piece. There are, of course, scientific disagreements.)

Other interesting questions on the topic however might be "How has human wound-licking have become culturalized in different ways? Outside of maternal grooming (like the mother kissing the boo boo in your example) are there any examples of cultures that practice wound licking on each other?"

On the latter question, there are various legends in Western culture about acts of healing being achieved through wound-licking, such as Emperor Vespasian's curing of the blind with his saliva or narratives about Francis of Assisi kissing lepers. But I'm not aware of any culture in history that had the popular practice of applying saliva to others' wounds -- I'd be interested if anyone has examples or thoughts about that.