There may be some AE/BE difference; in my family at least, if you spill hot coffee on yourself or the water in the sink faucet is too hot, you can say it burned you, you burned your hand. It may be technically scalding, but I think of that verb as being used more in cooking, like when you scald milk.
I wouldn't use 'wound,' though, unless it was a cut or something where the skin was broken; just 'the burn' is enough. You could say 'the burned place' or 'the place you scalded,' but not 'the scalding,' which would mean the act or process, not the result.
And just for the content, if you really are writing to someone about a painful accident that they suffered when doing something for you, the expected thing would be to say, again, how sorry you are that it happened.