Is the questioner liable to pay any remaining financial dues to the doctor, and must he inform the cashier of the reason if he is liable to pay anything?

We understand that the questioner suffers from obsessive doubts (waswasah), so we tell him: You must pay whatever is required of you to the female doctor based on custom or contract, and also if you acknowledge what she claims or if evidence has been established. You are not obligated to do more than this, for rights are not established merely by claims.

As for what concerns the institution, you are not obligated to fulfill its duties towards the hospital or the female doctor. There is no sin upon you if it deducts amounts from the hospital, and you are not required to investigate and inquire about matters that are between the institution and the hospital.