My doctor told me to come back for another test because he/she saw a shadow on my lung in the x-ray that I had in the annual check-up.
口語だとこんな言い回しが自然だと思います。
再検査＝another test, another exam(examination)
年一回の健康診断＝annual check up, annual physical exam, yearly check-up
he/she saw a shadow in the chest x-ray（胸部X線で影が見えた）と表現しても自然です。
come back for another testという風に「来てください」と言われることが多いですが、My doctor told me that I need another test-と言うこともできます。
It was told that my lung had a shadow on an X - ray during the annual health checkup and it was necessary to carry out a re - examination.
「年１回の健康診断のレントゲン写真で肺に影があり再検査が必要だと言われました。」
= It was told that my lung had a shadow on an X - ray during the annual health checkup and it was necessary to carry out a re - examination.
「年に1回の健康診断」= annual health checkup; annual checkup
「レントゲン写真」= x-Ray photograph
「肺」= a lung; lungs
「影」= shadow
「再検査」= re-examination
「〜が必要」= ~ is necessary
「言われました」= it was said (=I was told)
になります。
ご参考までに。
日本 
アメリカ合衆国 
