Protecting Our Children's Future Act of 2018 This bill amends the Congressional Budget Act of 1974 and other budget laws to make several changes to the federal budget process. The changes to the budget process include: converting the existing annual budget and appropriations process to a biennial process; changing the calendar period for the federal fiscal year (currently October 1 through September 30) to January 1 through December 31 beginning in 2020; requiring mandatory spending to be subject to the appropriations process beginning in FY2020, with exceptions for Social Security, Medicare, programs administered by the Department of Veterans Affairs, and TRICARE; requiring the baseline budget of each department or agency to be assumed to be zero and each proposed expenditure to be justified as if it were a new expenditure; requiring Congress to consider appropriations bills using procedures similar to the existing budget reconciliation process, which includes expedited procedures that prevent a filibuster and restrict amendments in the Senate; withholding pay for Members of Congress if the House and Senate have not jointly agreed to a congressional budget resolution by June 30 of the first year of a Congress; and repealing the existing discretionary spending limits and the sequestration process used to enforce the limits.