No, the olive oil will not increase your cholesterol. Animal fats are the chief culprit in dietary cholesterol. Flushing should improve the liver's ability to handle dietary fats.
The liver also generates cholesterol as a means of capturing toxins in the bowels. If you eat enough soluble fiber, the liver need not produce so much cholesterol.
Try eating a whole apple before every meal and one before bed. That will provide 50% of your daily fiber. The soluble fiber (pectin) in the apple may improve your cholesterol levels, soften hard bowel movements, and reduce the number of calories you eat during each meal.