That’s unfortunate, you should have spoken with a counselor at the school. Yes, you do have to report this F to dental schools, have you spoken with your pre-health advisor at your current school about this?
So game plan…talk with your current pre-health advisor for guidance/strategy, and contact the school where you took the summer class to see options for the summer school class…eg. if you retake there will they replace the grade? The audit idea is a good one, if they let you choose that at this point in the process, which is unlikely. Also if you were having issues that rise to the level of medical withdrawal, that sometimes can be changed after the fact, but you will have a W on the transcript (which is generally easier to deal with than an F).
Good luck and keep us updated.