First of all, change your name (TheindecisiveRN) to something funny, or strong, or beautiful, or cool... You don't want to be weak and hesitant nurse...
About your medical error.
As a new nurse you will have your number of mistakes. We all had that period of learning curve when we made mistakes. Just prey that your mistakes will not kill your patient; be super vigilant, question any medication to be given by you, find your favorite person you can ask about the medication you don't recognize; do not rush yourself-- it is better to be late than to make a mistake.
It is very good that you wrote yourself up after making mistake. It is better to reveal your mistake than let someone else do it for you.
The mistake you made is not that terrible. I noticed a few times that nurses for some reasons were late with Anti Xa: or the patient is a very difficult stick, or something else happened. A few hours of delay will not kill your patient. It is very good that you called and notified the doctor. They need to know why the result is this instead of that.
Tell yourself: "I can do it! I'll be the best nurse on my unit!" Do not let this incident put you down.
study. study. study.