Praise be to Allah.
Mixing of men and women in education, work or otherwise leads to serious consequences and many evils, and the harmful outcomes have become very clear and cannot be denied. Shaykh al-Islam ibn Taymiyah (may Allah have mercy on him) said:
If men mix with women, it is like fire mixing with wood. End quote from al-Istiqaamah (1/361)
For more information, please see the answer to question no. 1200.
Hence what you must do is look for a place where there is no mixing between men and women.
Covering the face and hands for women is a matter concerning which there is a difference of scholarly opinion. The most correct view is that on which fatwas on this website are based, which is that it is obligatory to cover them because of the evidence which has been explained in detail in fatwa no. 11774.
It is known that knowledge of medicine is a communal obligation, especially with regard to women learning gynaecology and obstetrics, so that there will be sufficient female Muslim doctors, which will spare women the problem of having to uncover their ‘awrahs in front of male doctors. The basic principle is that a woman is encouraged to study medicine in a proper environment that is controlled by Islamic guidelines. But if you have no opportunity to study medicine except by uncovering your face and hands on occasion, then there is no blame on you for that, especially since the obligation of covering the face and hands is a matter concerning which the scholars differed. The scholars have stated that concessions are allowed in the case of a woman studying medicine regarding matters that are more serious than that, such as uncovering ‘awrahs, touching them, and so on. This has been explained previously in fatwa no. 169979
But you must hasten to cover up again once the need has passed, and strive hard to avoid occasions of mixing and interacting with those with whom you are not obliged to interact and mix.
And Allah knows best.