purpleinopp said: Hi & welcome!
Dish soap is not the same thing as insecticidal soap. It's too bad this tidbit of info doesn't get around as much as the dish soap myth. At least you didn't put vinegar on it.
It looks like it is outside. Is it a shady spot? I don't know where you are, but Begonias should be kept away from too much sun in most places.
purpleinopp said: I don't know, Begonias don't even need much of a reason to freak out sometimes. Other members might have more experience with using those things on Begonias and what happened after.
I hope it improves!