United States-Mexico Border Environmental Protection Act - Establishes the United States-Mexico Border Environmental Protection Fund to be used by the Administrator of the Environmental Protection Agency (EPA) to investigate and respond to conditions which present a threat to the land, air, or water resources of the United States-Mexico border region. Authorizes the Administrator, whenever conditions exist which present a substantial threat to the land, air, or water resources in such region, to declare an environmental emergency. Prohibits the Administrator from declaring an emergency if the condition is within the sole jurisdiction of the International Boundary and Water Commission. Authorizes the Administrator to establish a system for information sharing and for early warning to the United States and affected States, political subdivisions, and Indian tribes of environmental problems affecting the United States-Mexico border region. Requires the Administrator to establish a United States-Mexico Border Environmental Protection Advisory Committee. Directs the Secretary of State, acting through the United States Commissioner, International Boundary and Water Commission, United States and Mexico, to conclude agreements with Mexico for the correction of and response to border sanitation problems in international streams forming or crossing the boundary between the United States and Mexico. Permits the Secretary to enter into agreements with Mexico to establish a binational advisory committee to assist EPA and SEDESOL in the monitoring and study of environmental conditions within the border region and make recommendations for ongoing environmental protection. Prohibits the expenditure of U.S. funds for emergency investigation or remediation in Mexico without a cost-sharing agreement unless the expenditure would be cost-effective and in the U.S. interest. Establishes the United States International Boundary and Water Commission Fund to carry out this Act. Authorizes appropriations.