Must I make up 11 days of fasting for every time I committed a specific sin after swearing an oath, knowing that I do not know the exact number of times?

Committing a sin is inherently impermissible. If you swore an oath to abandon a sin and then violated that oath, the sin's gravity increases due to the oath. The wording of the oath, "Every time I commit...", indicates repetition, which means you are obligated to fast for eleven days for each time you committed the sin, or pay an expiation for an oath for each time you broke it. If you do not know the exact number of times, the default is the exoneration of your responsibility, and you are only required to fast for the number of times you are certain of, because certainty is not dispelled by doubt. If you are ignorant of the number, then base your action on the minimum, as the default is the exoneration of responsibility.