Don't resign! Every nurse makes mistakes, especially when in a hurry. Go to the meeting with the manager and talk it out. Discuss how you could prevent this in the future. Clarify which drips need a double check (and when in doubt for any drip, double check if you're unsure of the setup).
Do you scan your meds? If so, why did the computer did not prompt you to have another nurse double sign off if that is required? I would ask if a safety measure such as this could be put in place.
What do you do to cope with stress and relax? Maybe read a book, take a bubble bath? Take a deep breath and try to relax.