Benefits vary somewhat from one hospital/facility to another, so there's no one, specific answer to your question. However, having said that, it's fairly typical for many (most?) hospitals to offer new employees (new grads or otherwise) two weeks of vacation time (with additional weeks after some specified number of years of employment), and 12 days (1 day/month) of sick time. However, those figures are typically calculated on 8-hour days (i.e., 80 hours of vacation time and 96 hours of sick time), so it works out to fewer "days" if you're working 12 hour shifts.
Most places allow you to accrue sick time indefinitely (no point at which you start "losing" hours), but you don't get paid for accumulated sick time if/when you leave your job. Many organizations set a limit on how much vacation time you can accrue, and, at some specified point, you automatically either get paid for or just lose (depending on how civilized and generous your employer is) the additional hours. The number of hours you can accumulate is usually pretty high, though (like, maybe, six months worth of time); not "use it or lose it" from one year to the next. Typically/traditionally, you do get paid for your accumulated vacation hours when you leave the job.
Having said that, again, there is no hard, fast rule -- employers are free to offer whatever benefits they choose. Seems like a growing number of employers lately are offering a straight "PTO" benefit like you described -- a single "bank" of hours that you can use for either sickness or vacation.
In general, smaller outfits like doctor's offices offer fewer and less generous benefits than hospitals and other large employers. Public (city/county/state/federal) agencies tend to offer more generous benefits than private employers (again, not a hard, fast rule