I do not know of an expedited process for green cards where healthcare workers are concerned, although USCIS recently said that it would expedite employment authorization renewal cards for such workers. The fact that you are already in the US instead of overseas would also not be in your favor in requesting an expedite from the agency. The expedite criteria from USCIS are:
Severe financial loss to a company or person, provided that the need for urgent action is not the result of the petitioner’s or applicant’s failure: (1) to timely file the benefit request; or (2) to timely respond to any requests for additional evidence;
Emergencies and urgent humanitarian reasons;
Nonprofit organization (as designated by the Internal Revenue Service (IRS)) whose request is in furtherance of the cultural or social interests of the United States;
S. government interests (including cases identified as urgent by federal agencies such as the U.S. Department of Defense (DOD), U.S. Department of Labor (DOL), National Labor Relations Board (NLRB), the Equal Employment Opportunity Commission (EEOC), the U.S. Department of Justice (DOJ), the U.S. Department of State (DOS), DHS, or other public safety or national security interests); or
Clear USCIS error.
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