When I worked PCU/med tele in my first year out of school, I never left on time. Why? I tried to get everything done that I was supposed to, and most certainly never signed off anything that I didn't do. The work load was horrendous - 12 hours shifts, 8 beds for one nurse and aide, sometimes 4 discharges and 4 admits in the middle of the day, no IV team, dopamine and Cardizem drips to titrate, never mind the codes and other unexpected happenings - and I routinely worked 13, 14, 15 (rarely, 16 or 17 hours) with only a 30 min lunch break (which I always took, otherwise I wouldn't have lasted as long as I did - 11 months). I did get OT, however, and it was never questioned by management (my manager, the best one I ever had, left soon after I did because she couldn't do anything about these conditions).
However, many other nurses did leave on time - some never left a minute late, even new grads! Why? No, they weren't geniuses, and no, they didn't know the secret to "time management". The left on time because they took short-cuts - much of what they charted never got done. One new grad never missed a breakfast break - in the middle of the morning med pass! Everyone knew he was a lousy nurse (still is to this day - he works in my current hospital now), but by golly, he always left on time.
So don't feel bad, the problem is theirs, not yours. I does sound that your manager is not understanding (or trying to force you to do something that is against your ethics - shortcuts, etc.), so you may have to do what I eventually did - run, don't walk out of there. I hope that this isn't the case, but if it is, it may be better to quit sooner rather than later (and don't worry about your resume, nobody would hold it against you). Perhaps you could also transfer to a slower-paced unit, such as outpatient surgery.
Best of luck to you!