Ooooohhh. This is tricky. Turnitin has really complicated things. My gut reaction would be to start fresh with new admissions essays because it would not be worth the risk of someone checking and thinking you had taken someone else's work. For a good writer, which you must be if you have submitted to contests, the writing should come easy. THEN you can cut and paste and switch those essays around without worry.
What you are doing, in my opinion, is absolutely right. The dilemma is with Turnitin; someone might check it and not know that it was your work all along.
At my daughter's school four years ago, they worked on essays in their junior year English classes that could be used for college essays. However, they were never submitted to Turnitin. I think she used part of her class essays for admissions.
Today, the risk of someone checking is small. The question you have to ask yourself is this: would you rather just take the time and write new essays or worry all admissions season that someone may think you lifted your essays? Best wishes. This is an unintended complication of Turnitin, IMO.