To ujm: The public official who brought down inflation in the Carter-Reagan years was Carter appointee Paul Volcker, head of the Federal Reserve Board. Learn some facts.
As for oil prices, they are set by world markets. If American companies find more oil, they will sell it at world market prices. And, no, if American companies find more oil or gas, it is unlikely to increase world supplies so much that prices go lower. Only Saudi Arabia can pump or withhold enough oil to impact world prices.
One other popular proposal – eliminate gas taxes – is a temporary fix at best, as we need tax revenue to maintain the roads.