Thank you for your kind words and responses.
Final word: They rescinded my offer. To say I am devastated is an understatement. They quoted policy and basically said thanks for your honesty but per policy, we have to rescind your admission. Basically, since the F dropped my GPA at all, it was no longer the GPA they chose to admit me with.
I guess I am updating this for anyone that has a similar situation in the future and is frantically searching this site for someone who might have had a similar situation.
I guess the lesson here is honesty isn’t the best policy? I outed myself without waiting to see what they were really looking for. If I had held my tongue I would be going to my dream school.
But the real lesson I suppose is to make sure you triple-check that you didn’t omit any information on accident (don’t omit on purpose either), or you might end up sad like me.