Protecting Seniors Through Immunization Act of 2019 This bill specifies that certain deductible, coinsurance, initial coverage limit, and cost-sharing requirements that apply under the Medicare prescription drug benefit shall not apply with respect to vaccines that are recommended by the Advisory Committee on Immunization Practices of the Centers for Disease Control and Prevention. The Centers for Medicare & Medicaid Services must provide to Medicare beneficiaries specified information regarding (1) coverage of vaccines for seniors, and (2) access to recommended vaccines without cost-sharing.