NO! We are a net exporter of refined products. We refine a bit more than we currently consume. We are exporting about a million per day of products but we are importing about 9 million barrels per day of oil.
Combined, we are still a major importer of Petroleum, crude and products together.
Our total net imports (taking credit for our exports) still exceeds our domestic oil production. We would have to more than double before we reached an point of no net imports.
We also sell refined products to countries that have a very high demand and do not have adequate refinery capacity themselves. That is why the price is going up when our actual national consumption is down. (Supply and Demand)
There was a recent surplus if distilled products left over from the last glut, which is why the actual price of crude was going up but Gas prices stayed low and even dropped. Now that the inventory has been sold and moved, prices are equalizing more in line with the volume and price of crude.