Where I work, people stopped considering me a new grad about a year out. At the minimum an employer might consider you not as "new-gradish" after 6 months, but, really, you need a year.
I've never seen a nursing job advert that states "at least 6 months experience." Leaving your first job at the 3 month mark does not look good for you. Give your current employment situation at least 6 months. It's going to take time before you really hone your prioritization and time management skills.
I started out in the ER, but after my orientation, I felt that I was running around considerably more than my fellow nurses. After a year, I felt like I wasn't wasting as much time. My nursing school
buddies who did start out in med-surg lamented about the same things you are. After about 8-9 months they started to get a handle on time management and weren't having to stay late so often.
Hang in there. You'll be better off for it!