Wow, Michlynn, what a horrible situation. I echo others responses and say you were indeed thrown under the bus because they were looking for people to blame. Easy to blame the new grad RN who feels terrible instead looking closely at the system they have for med passes and looking at the training they provide to new staff.
Yes, you committed a "med error" but in the grand scheme of things, OD'ing on narcan is almost laughable. The dose is max of 2mg every few minutes, generally max of 10mg. 3.2 mg is being blown out of proportion. And it sounds like the oxycodone was just given minutes before the narcs so there wasn't much to reverse just yet. I was once on shift when a nurse rapidly pushed narcan, the patient became very agitated, developed pulmonary edema and when he came to was very angry because its so unpleasant to be reversed rapidly and it shouldn't be done. You committed a med error and immediately owned up to it and feel remorse. That's something to be proud of, some would cover it up, especially if they were aware of such a punitive system for handling errors.
If the place you interviewed with asked more questions about why the last place didn't work out, I would consider telling them the basics of what happened and that you told management right away and feel terrible about it. Be prepared to tell them what you learned from it as well such as, "If I push a drug, I am responsible for making sure it is a safe dose and pushed over the right time frame" and in the future, "I would take the 30 seconds to look up the drug, find another person to push the drug who is familiar with it etc etc".
If they don't ask anymore details though, I wouldn't offer it. It varies by state what a previous employer may tell a prospective employer, where I live it is minimal, the dates they worked and whether you would hire them again.
Good luck with future employement.