If someone has “got you over a barrel,” it implies they’re in control and you’re not. People rescued from near-drownings used to be draped a barrel while the water was cleared from their lungs. However, in the more sinister situations which likely inspired the term, people were put over barrels and tied in this position to receive beatings.
Since booze often used to be shipped in barrels, “barrel fever” can be sickness from excessive drinking, a hangover, or in the longer term, the physical debilitation which often comes with chronic drinking.
Perhaps you’ve recklessly gone barrelling down the highway in your car, but this term likely comes from the wooden vehicle. Back when barrels were common in households and farms, thrill-seeking youngsters would climb in and roll down hills. You cannot steer nor stop the average barrel from inside, so this pastime was rather dangerous.