No, placebos don't work.

That is not what is meant by "the placebo effect" by doctors. There is no active ingredient in a placebo. That's why it has no effect on broken bones or cancer. A placebo doesn't have an effect on anything.

However, patients that receive treatment that include a placebo medication and/or procedure (instead of the active version) often report improvement in their perception of their condition. Including pain, nausea, depression, and anxiety. The patients report feeling better.

This "feeling better" after receiving a fake treatment is the placebo effect.

The reason a kiss and a hug works so well on kids (and adults) is that it is comforting and loving. It makes them feel safe and secure and cared for, lowering their anxiety and indeed pain.