I would argue that a variation of "When did it start to hurt?" should be accepted, although I acknowledge that it is a fairly liberal translation for this.
I imagine the course admins would like to not accept this since it would correspond better to another Swedish phrase (när började det göra ont?), and it has some pedagogical purpose to separate the two.
Could I use here ''ont'' instead of ''smärta''? What are the differences btw them?
smärta is a noun, like 'pain'.
ont is normally only used as an adverb: det gör ont means 'it hurts'.
To have ont in this sentence, you could say När började det göra ont? 'When did it start to hurt?'