Hmmmm. In my experience most facilities give employees a "leeway"time- usually 6 minutes to clock in either before or after their scheduled time. You did not mention the nature of your tardiness so we can only guess. Were you a half hour late? An hour? 20 minutes? Was this once per week? Per pay period? Sorry sweetie but you own some of this. We unfortunately do not work in a profession that allows us to stroll in, from time to time, a bit late. But I am not going to bust your chops because I know that you already feel badly about the entire experience. The best thing to do is to admit you made some mistakes and move on. You can not play the victim because playing the victim will not get you a new job.
First, polish up that resume. Second, think long and hard about the work environment and what your needs are. If you need a flexible job where running just a few minutes late isn't going to make or break you then consider a job that will allow for that. If you need a calmer work environment then consider a job that might allow for a slower pace. If you need a job that maybe isn't so people-oriented then consider it. We are blessed to have so many opportunities in our profession: IT Nursing, bedside nursing, home care, clinic/out-patient care, specialized care, etc. When you decide what you need to do, then it is enough to chalk up the last job as maybe not being a good "fit". Good luck!