Since Miriam Gregg is not a registered nurse she is either a LPN (Licensed Practical Nurse) or a CNA (Certified Nursing Assistant), so she should not be filling syringes or preparing any type of medication. Only doctors, certified physician assistants (PA-C), nurse practitioners (NP), pharmacists and registered nurses can prepare medications (prepare meaning measuring dosage like when filling a syringe or an IV bag, or mixing a oral solution). A LPN can administer a intravenous medication if it has been prepared by a physician, PA-C, NP, pharmacist or a RN and can start IV's but they cannot prepare medication and can only administer it under supervision. A CNA cannot handle medications or start IV's under any circumstances.
Speaking about Dr. Elizabeth Olivet, Detective Logan remarked: "She's a psychologist . . ." Dr. Olivet has been portrayed throughout the series as a physician, board certified in psychiatry. In order to function fully within a large metropolitan law enforcement's jurisdiction, a physician is required to speak to both psychiatric as well as psychological disorders. Psychologists cannot treat mental illnesses that fall into the category of medically managed psychiatric illness.