Gulf Coast Hurricane Aid Act of 2021 This bill provides emergency assistance for disaster response and recovery and other expenses directly related to Hurricanes Laura, Delta, and Zeta and flooding in calendar year 2021 in Louisiana. Specifically, the bill provides funding for the Social Services Block Grant for such response, recovery, and expenses. The distribution of grant funds are limited to states directly affected by the hurricanes and flooding. The Department of Health and Human Services must distribute such funds to those states based on demonstrated need in accordance with objective criteria that are made available to the public. Further, such funds may be used for health services (including mental health services), and for costs of renovating, repairing, or rebuilding health care facilities, child care facilities, or other social services facilities. The bill also provides emergency assistance through the Community Development Block Grant program. The amounts provided by the bill are designated as an emergency requirement pursuant to the Statutory Pay-As-You-Go Act of 2010 (PAYGO) and the Senate PAYGO rule. (This exempts the budget effects from being counted for the purposes of enforcing the PAYGO rules.)