Toxic Exposure Education for Servicemembers Act of 2022 This bill requires the Department of Defense (DOD) to establish a new risk assessment for toxic exposure for members of the Armed Forces who are assigned to work near burn pits. DOD must also establish an outreach program to inform such members regarding toxic exposure. Additionally, DOD must publish on its website a list of resources for members and veterans who experienced toxic exposure while serving as a member of the Armed Forces, dependents and caregivers of such members and veterans, and survivors of such members and veterans who received death benefits.