If a woman needs medical care that exposes part of her body to a male doctor, does she still have an obligation to keep other parts modestly covered? For example, during a gynecological exam, must a married woman keep her hair covered? Etc.

Shalom Uveracha, Women are allowed to visit male doctors if there is no female equivalent available even if he must touch her and examine her. The reason for this is that the doctor is doing his job and thus there are not sexual overtones of this contact. However the fact that a woman has to reveal part of her body for examination does in no way allow her to reveal other parts that are not part of the treatment. Kol Tuv