Health Care Emergency Guarantee Act This bill requires the Department of Health and Human Services (HHS) to pay the out-of-pocket expenses of individuals receiving medically-necessary care or services during the COVID-19 (i.e., coronavirus disease 2019) pandemic. Specifically, the bill covers the costs for services provided through public or private health insurance and to uninsured individuals, including prescription drugs and care related to COVID-19, beginning on the date of enactment of this bill until a COVID-19 vaccine is widely available to the public. Health insurance plans are prohibited from increasing the cost-sharing requirements of plans while this program is in effect and HHS must report to Congress on the program on a weekly basis.