What is the ruling regarding my being compelled to expose my body to male non-Muslim doctors to ascertain my well-being in the context of applying for a job, and what is required of me by way of expiation for this act?

If a Muslim female doctor is not available, the priority is a non-Muslim female doctor, then a trustworthy Muslim male doctor, and then a non-Muslim male doctor out of necessity. It is not permissible for you to be alone with a man who is not your husband or a mahram (definition). If you have gone to these doctors without seeking a female doctor, you have committed a sin and must repent and seek forgiveness. Allah the Almighty said: (And whoever does evil or wrongs himself then seeks forgiveness of Allah will find Allah Forgiving and Merciful) [An-Nisa: 110]. The Prophet, peace and blessings be upon him, said: "O Aisha, if you have committed a sin, then seek Allah's forgiveness, for repentance from sin is remorse and seeking forgiveness."