Nobody has a real answer because this is the TRAVEL forum, not the career counseling office. We're travel experts, not HR staffers.
My advice would be to post something in the medical forums, where you have actual doctors.
As for the last part of your question, there are HUNDREDS of hospitals and medical centers in the LA area, and listing them would be too exhaustive. Here are the hospitals just in southern LA county alone:
Avalon Municipal Hospital — Catalina
Baldwin Park Hospital — Baldwin Park
Bellflower Medical Center — Bellflower
Beverly Hospital — Montebello
Brotman Medical Center — Culver City
Casa Colina Hospital For Rehab Medicine — Pomona
Centinela Freeman Regional Medical Center, Centinela Campus — Inglewood
Centinela Freeman Regional Medical Center, Marina Campus — Marina del Rey
Centinela Freeman Regional Medical Center, Memorial Campus — Inglewood
Citrus Valley Medical Center - QV Campus — West Covina
Citrus Valley Medical Center - IC Campus — Covina
Coast Plaza Doctors Hospital — Norwalk
College Hospital — Cerritos
Community Hospital Of Gardena — Gardena
Community Hospital of Huntington Park — Huntington Park
Community Hospital of Long Beach — Long Beach
Doctors Hospital Of West Covina — West Covina
Downey Regional Medical Center — Downey
East Los Angeles Doctors Hospital — East Los Angeles
Foothill Presbyterian Hospital-Johnston Memorial —
Greater El Monte Community Hospital — South El Monte
Harbor-UCLA Medical Center - West Carson
Kaiser Foundation Hospital - Bellflower — Bellflower
Kaiser Foundation Hospital - Carson — Carson
Kaiser Foundation Hospital - Harbor City — Harbor City
Kaiser Permanente Medical Center/Baldwin Park — Baldwin Park
Little Company of Mary Hospital — San Pedro
Little Company of Mary Hospital — Torrance
Long Beach Community Hospital — Long Beach
Long Beach Doctors Hospital — Long Beach (closed, June 1998)
Long Beach Memorial Medical Center — Long Beach
Los Angeles Community Hospital of Norwalk — Norwalk
Los Angeles Metropolitan Med Center - Hawthorne Campus — Hawthorne
Martin Luther King Jr.-Harbor Hospital — Willowbrook
Memorial Hospital Of Gardena — Gardena
Metropolitan State Hospital — Norwalk
Miller Children's Hospital — Long Beach
Mission Hospital of Huntington Park — Huntington Park
Pacific Hospital Of Long Beach — Long Beach
Pomona Valley Hospital Medical Center
Presbyterian Intercommunity Hospital
Rancho Los Amigos National Rehabilitation Center — Downey
Regional Medical Center - South Street
San Peninsula Hospital
San Dimas Community Hospital
Speciality Hospital Of So. Ca.-San Gabriel Valley
Specialty Hospital Of Southern California
St. Francis Medical Center — Lynwood
St. Mary Medical Center — Long Beach
Suburban Medical Center
Torrance Memorial Medical Center
Tri-Cities Hospital
Whittier Hospital Medical Center