Securing Our Schools Act of 2023 This bill provides funding and resources to (1) strengthen security on school premises, and (2) provide access to student mental health resources. It also generally prohibits the use of federal funding provided by this bill for abortions. Specifically, the bill provides specified funds through FY2033 to the Department of Education (ED) for Student Support and Academic Enrichment grants. It also directs ED to use a portion of these funds to strengthen security on school premises. The bill reauthorizes through FY2029 the Nonprofit Security Grant Program and revises the program, including by increasing grant amounts for administrative costs and technical assistance. Further, the bill allows funds under the Community Oriented Policing Services grant program to be used to pay for school resource officers and improve physical security at schools. Additionally, the bill transfers specified funds under the American Rescue Plan (ARP) Act to ED to establish the Student Access to Mental Health Program Fund, through which ED must award grants to states to support the salary of a mental health professional in eligible schools; and specified unobligated funds under the ARP Act to support certain mental health programs of ED, the Department of Health and Human Services, and the Substance Abuse and Mental Health Services Administration. The Government Accountability Office must conduct a study on mental health providers in schools. The bill transfers specified unobligated funds that were provided to address COVID-19 to ED to carry out this bill.