Olivia Ambrose, 23, was last seen on Saturday night. Her family says she missed a medical appointment on Monday, which is out of character.
The union and LA Unified School District are at odds over issues including salary, class size and support staff.
The second victim of last week's incident at Taos Ski Valley, New Mexico, is dead, relatives said, while another was killed Monday near Aspen, Colorado.
The unidentified physicians were responsible for the woman’s care, Hacienda HealthCare said in a brief statement.
Authorities are investigating threats against some of the students at the school.