Not a placebo effect, Health. I have over my six decades burned my hand on many a stupid occasion, and other so-called burn ointments did zip (and certain types of ointments can make the burn worse). Stuff like Solarcaine, etc. never really helped except for a minute or so. Silvadene was the only effective treatment we have ever used, and it TOTALLY stopped the pain.
For a more serious burn, a doctor should ALWAYS be consulted, as infection could set in, and there might be more damage to the underlayers of skin. And if it is chas v’sholom a child who is injured, I don’t care how minor the burn seems, I would call the doctor.