Iran and Hizballah Western Hemisphere Prevention Act of 2017 This bill declares it to be U.S. policy to prevent further penetration of Iran and Hizballah into the Western Hemisphere and to prioritize diplomatic efforts to engage countries in the hemisphere to disrupt and degrade Hizballah's illicit networks operating in the region. The Department of State shall submit a strategy to prevent hostile activities by Iran and disrupt and degrade Hizballah's illicit networks in the hemisphere. The President shall instruct the State Department to prioritize U.S. diplomatic engagement with countries in the hemisphere in order to increase cooperation and build the capacity of the governments of those countries to prevent such activities and disrupt and degrade such networks. The bill amends the Hizballah International Financing Prevention Act of 2015 to require the President to instruct: the U.S. Permanent Representative to the Organization of American States (OAS) to work to secure OAS support for a resolution that would declare Hizballah to be a terrorist organization and address such illicit networks; and the U.S. Ambassador to the Organization for Security and Cooperation in Europe (OSCE) to work in securing a report on compliance by participating states with OSCE Decision Number 1063, the Consolidated Framework for the Fight Against Terrorism, with regard to Hizballah; and U.S. diplomats to work with international forums to identify government entities in Latin America and the Caribbean that support individuals affiliated with Hizballah in the hemisphere. The State Department must provide to the relevant congressional committees annual briefings that review its efforts to implement such strategy and U.S. bilateral and multilateral engagement with respect to Hizballah in the hemisphere.