A nurse exposing her arms during her work in the hospital
In the name of Allah, the most Beneficent, the most Merciful.
There are two conditions, which needs to be found for one to determine whether it will be allowed for him or her to work in a particular place. The first condition is that one has to make sure the nature of the job is lawful where it does not contradict any teachings of Islam and nor is he or she entailed to do anything unlawful in performing the job. The second condition is that the wages for the job comes from a lawful source.
With regards to your question, you are being asked to do something unlawful by exposing your arms at work. It is obligatory for a woman to conceal all her body parts in front of a non-mahram (those with whom marriage is lawful) except the face, hands and feet. (Raddul Muhtar p.531 v.9) And in this day and age due to the fear of temptation it becomes obligatory to cover their face as well.
Allahmah Ibn Abeedeen Shami (RA) has said: (“A young woman will be prevented from exposing her face) not because it is part of the awrah, rather (for the fear of temptation.”) (Raddul Muhtar p.532 v.9)
In the meantime you can work there until you find a job, which does not entail you to do something unlawful. Pray to Allah and seek repentance for the unlawful thing, which you are being told to do.
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham.