He/She was playing outside and was hit in the groin by some playground equipment and it started bleeding.
He/She hit himself in the crotch with some playground equipment and started bleeding.
股 = groin, crotch (両方とも「股間」というニュアンス)、between the legs
遊具 = playground equipment
出血した = bled, was bleeding
「外で遊んでいて、遊具で股を打ち出血した」= He/She was playing outside and was hit in the groin by some playground equipment and it started bleeding.
He/She hit himself in the crotch with some playground equipment and started bleeding.
その二つの言い方は通じると思います。^^
「股を打つ」という表現は英語では "hurt his groin" と言います。「遊具で」という部分は "on the playground equipment" とします。
したがって、「遊具で股を打った」という状況を説明するときは "He hurt his groin on the playground equipment." と言うと良いでしょう。この表現は中立的であり、医師や親など、誰でも使うことができます。
他にも "He injured his groin on the playground equipment." や "He bruised his groin on the playground equipment." と言うこともできます。