Diagnosis of Measles is usually done via serology —looking for measles antibodies in blood serum, and the disease is usually most likely to occur among unvaccinated individuals.
Labs including full blood count, liver enzymes and serology can be useful to identify the cause and an upper GI Endoscopy can identify esophageal varices in order to treat them appropriately.
Let's start with the FDA which has a page about emergency use authorizations and if you scroll down, what you see is that there are 7 that have been approved for serology.