Sorry to hear about your diagnosis.
People have expedited for health reasons for the USC petitioner, yes. You need to write a succinct letter explaining the situation, and providing supporting documentation, such as a letter from your oncologist. I am an oncology RN, and we have provided such letters to patients for immigration purposes.
Good point.
OP, what is the visa category? If a visa is not numerically available at this time, they cannot expedite it for any reason.