National Informed Consent Exemption (NICE) Act This bill restricts the federal government and federally funded entities from mandating that U.S. citizens receive a vaccination or a test for an infectious disease in order to participate in federal programs or activities such as travel. It also specifies that laws, regulations, or policies that discriminate on the basis of a citizen's vaccination status are unenforceable, subject to limited exceptions. The bill establishes a national vaccination exemption that may be exercised by any individual, including on behalf of the individual's children or dependents. Further, the bill prohibits vaccinating a child without the consent of each parent or guardian. One parent or guardian may consent if the other parent or guardian received, at least three days prior, written notice of the child's vaccination appointment. The bill's provisions do not apply (1) to lawfully incarcerated or institutionalized individuals, (2) to a specific individual subject to an individualized court order that meets due process protections, or (3) during declared emergencies if the jurisdiction's governing authority formally applies to the President for an exception to the national vaccination exemption that meets specified standards. An aggrieved individual may enforce the bill through a private right of action. Additionally, an entity that provides false information to influence an individual's decision about receiving a vaccine shall be liable for damages resulting from the vaccination. The Surgeon General must establish an independent commission to evaluate the safety of COVID-19 vaccines and other vaccines recommended by the Centers for Disease Control and Prevention.