I work as a nurse and in my work I see men and women's private areas, not out of choice but because of the nature of my work. Could you please let me know what the Islamic view on this, as I am extremely worried about this sensitive issue?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is permissible for a woman to work as a nurse for women only but looking at their Awrah (those parts of body that must be covered) is forbidden. The Awrah of a woman to another woman is from navel to knee. However, looking at Awrah only at the time of necessity is permissible.
As for working as nurse for men, it is not permissible at all with the exception of dire necessity. Imam Ibn Hajar said: 'A woman can treat alien men at the time of necessity which is estimated only to the extent of its direness as far as the matter of looking and touching is concerned'.
The evidence for the given stand is the Hadith reported by Imam al-Bukhari from Rubai Bint Muawadh who said: "We used to go for military expeditions along with Allah's Apostle and provide the people with water, serve them and bring the dead and the wounded back to al-Madinah" .
Therefore, it is not permissible for you to treat alien men except if there is a dire need such as the lack of male nurses or they are not capable to deal with the patients, or you cannot get food, clothes and the like except through this profession.
If there are male nurses who can carry out the task and you are not in need of such work, then it is better for you to give up such a work and stay at home or you may seek another work suited to the nature of a woman and free from the prohibitions of Shari'a. Allah Says (interpretation of meaning): {… And whosoever fears Allâh and keeps his duty to Him, He will make a way for him to get out (from every difficulty). And He will provide him from (sources) he never could imagine. …} [65:2-3].
The one who gives up something for the sake of Allah surely, Allah will grant him better than what he has left.
Allah knows best.