I want to make this right. I want to do better. I need to talk to my manager and preceptor and tell them I was wrong and I'm sorry. That is very hard for me to do since I dont usually have the humility to such a thing. I realize it is what I need to do though.
You said it all right there. Honesty with humility is the only way to appeal to your manager and preceptor. An open heart and mind is the only way to succeed in your current position. It may take awhile for your other co-workers to believe your sincerity, so you must be consistent every day as you truly pursue your best. Continue being humble, respecting the experience of others and genuinely seeking to learn from them. Good luck to you, you have already jumped the highest hurdle - realizing your mistakes and admitting them, and realizing what you need to do.
Hang in there! Some day in the future you will doubtless be helping other new grads through similar situations, and you will be the one with the experience and advice.