Patient Identifying Information Confidentiality Act of 1988 - Amends the Public Health Service Act to direct the Secretary of Health and Human Services, before disclosing to the Congress any medical record acquired or created by the Public Health Service, to delete identifying information in the record, unless the individual identified gives written consent. Directs the Secretary, for the purposes of cross-referencing the medical records pertaining to a particular individual, to establish by rule a system by which such records may be identified without using identifying information.