The US is not in a position to process much of the sweet crude it has. Instead, imports sour crude, which is what much of the US's refineries are actually built to handle. This is why Venezuela was such a thorn in the side of the US, as they were one of the major producers and also largely produced sour crude.

As adwn says, it's a globally priced commodity, and the US is not in a position to disentangle itself from that market because in spite of being one of the world's largest producers, US refineries are not in a position to process that product, so it needs to go abroad. The US needs to import significant amounts of sour crude to be refined for their own use.

The US is just as screwed as the rest of us.

Also, the primary worry for Europe isn't oil, it's natural gas.

Oil is a globally priced commodity. This means that downstream consumers of oil in the US will be just as affected by rising prices as European consumers. US producers of oil will benefit, though.