What should one do if they experience a wet dream during their night shift and cannot find a way to perform ghusl to cleanse themselves from janabah? And is it permissible for them to perform tayammum?

Ghusl is not limited to using a shower; a person can perform Ghusl by pouring water from a vessel or the like. It is not permissible to remain in a state of Janabah until the Fajr prayer is missed. Likewise, Tayammum is not permissible when water is available and one is able to use it without harm.