I think reading to the kids is a great idea.

I think the scalding water story is possibly a good one.
If anyone asks/asked me about scars, I usually say something like "it's old" "it's healing" or "it's only a burn".
Generally that stops the conversation.

Skeezyks is wise, treatment should be a priority as infection would make the scars much worse and the correct dressings will heal it more quickly with less scar.

I may have been lucky, but in my experience, when health professionals have asked me about burns, either because they noticed them in another context or I sought treatment for them myself, the main concern was to make sure I was not a victim of domestic violence and someone else was doing it to me. Some professionals are insensitive and treat people badly, but I wonder if Sometimes our guilty feelings makes us super sensitive to what we think they are thinking about or judging us, even if they're not.

Best wishes and hugs