Small Business COVID Relief Act of 2022 This bill provides support for restaurants and other businesses impacted by the COVID-19 pandemic. Specifically, the bill provides additional funding for the Small Business Administration (SBA) to provide grants to support the ongoing operations of eligible restaurants and similar establishments. The SBA must report weekly and biweekly information about grant applications, awards, and denials. Additionally, the bill funds grants to support other eligible businesses impacted by the pandemic, including gyms and fitness centers, minor league sports teams, businesses located near land ports of entry, businesses that provide and support live events, and businesses located in certain U.S. exclaves with limited accessibility. A business may receive a grant under only one program. The bill also establishes procedures for the SBA to implement and provide administrative support for these grant programs. The SBA must institute an oversight and audit plan to review the use of grants under these programs. Further, the bill provides additional funding for grants to support eligible transportation service providers. Finally, the bill designates the funding as emergency spending, which is exempt from discretionary spending limits.