First of all, well done on immediately admitting your error, that is the number one rule!
I'll be honest, in my first two months of nursing (been doing it 3 1/2 years now), I made a huge error of giving actrapid instead of insulin to a pt. I realised immediately, admitted my error and thankfully the only action necessary was hourly blood sugars for the patient.
I was referred to the director of nursing (not sure what the head of nursing in the US is). They congratulated me on admitting everything, but was put under supervision on all aspects of my nursing care for three months, getting a personal shift report after every shift. I didn't have one bad report, but the supervision scared the heck out of me and I am sooo careful now! I believe the senior nurse who checked the drug with me got a worse fate, at least she wouldn't talk to me after that and left shortly after
Don't think about leaving nursing at all, we ALL make mistakes, the difference between a bad nurse and a good nurse is the bad nurse will cover it up and not change her practice. Try to find a preceptor at work or someone who will guide you in your practice and above all, try not to worry, that's when errors really do happen!