I am a newly graduated training professional in the medical field, and am currently working in a hospital and when on wards and seeing patients, it is strictly required to roll our sleeves up to the elbow for ‘infection control’. As a female Muslim, I observe the hijab and was wondering whether this would be permissible.
And if not, does this mean a female Muslim can not pursue a career in the medical field (this includes doctors, pharmacists, nurses etc)

Female Muslims are allowed to pursue medical fields. However, Islamic etiquettes must be upheld at all times during services or works.

Your situation: this is definitely not permissible under normal circumstance. Try to avoid it as much as possible. However, there is no harm in doing it if it’s completely beyond your control and it’s per the medical practice country wide.