"After the boy fell, his knee started to bleed."
Translation:Post kiam la knabo falis, lia genuo komencis sangi.
Because "the surgery" is a noun phrase which can take a preposition but "the boy fell" is a clause (with a verb) and so needs a conjunction.
If it helps, you can try to replace "before/after" with "because", because there English makes a difference between conjunction and preposition: "because the boy fell" but "because OF the surgery".
So if you would have to say "because of", you would use just "antaŭ/post" in Esperanto for "before/after", while if you would have to say "because" without "of", it will be "antaŭ ol/post kiam" with an additional word in Esperanto.