Before I give any meds I've given before, with my IV ones, I ALWAYS check the yellow bible - our big IV drug book in Oz - tells u everything on how to give all drugs, dosages, routes, times, etc. Get into the habit of double-checking everything. With drugs u haven't given before, check them on MIMS - never give a drug w/out checking it if unsure.
If the Dr ordered it as you gave it, it isn't your fault if ur new, though ur supposed to know dosages & what ur giving, etc but sounds like the Dr is liable.
One last piece of advice: DO NOT EVER GIVE DRUGS IN A HURRY, even if pressured by other nurses, NUM, family or the patient, or even if u get behind. It is better to give a drug late, than to give the wrong drug, or give it by the wrong route, etc. Always go thru your drug checks - even if u know the patient & have given that drug numerous times. I never get blase with drugs - once you inject the wrong drug, that is it. I nearly DID give too much of a drug not long ago - it was the way the chart was written, you could interpret it 2 ways. I gave 2 x of a drug when the Dr wanted it given over separate periods during the day (this wasn't written down). Also Drs ARE to blame, cos they make up their own drug shorthand, which is DANGEROUS.
You are being very hard on yourself sweetie. You are only new, you reported what had happened and don't worry re the paperwork: the hospital must follow procedure & legally report incidents. You are NOT HOPELESS - we have all made mistakes. Have a plan to follow for ur work - a cheat sheet - to help u get organised. I KNOW how hard the ED/ER is - I'm a RGN learning ED/ER as well, and there is a lot to take in. Just be a bit more assertive & take control of ur patients & your work - or it takes control of you. You won't know everything, but ask many questions & tell people ur new - they will understand.
Do not beat yourself up so much. Learning takes experience, and you won't ever know everything.
Just keep plodding along, go a bit slower & have a plan on your shift, and you should be OK.