構文は全然問題ありませんが、以下の単語は修正が必要だと思います。
また、「もう少し早く」が英訳されていません。
減点個所:
① looked(過去分詞) → checked(過去分詞) ※check … …(の状態)を確認する /look 見える
② they → it (=the injured knee)
③ もう少し早く → a little earlier
⇒ If I had had my injured knee checked at the hospital a little earlier, it would have healed in about a week.
【別解答】
My knee injury would have healed in about a week if I had had it checked at the hospital a little earlier.
参考にしてください。