1. Doesn't sound like an ethnicity issue, more like a white women being extra and bored. It's definitely condescending but those **** would likely do the same thing to any nurse they see as inferior to them. Nurses are cutthroat, vicious, think they know you better than you know you, and this can be interpreted as racism. Which it might be but I highly doubt these girls hold a prejudice against tan people. Those same girls go to extreme lengths to become tan. It's not a skin color thing
2. Read the 48 Laws of Power; I'm serious, this book explains all human behavior
3. Coworkers doing your job for you is a good thing. If you have good enough social skills you can get coworkers to do a significant amount of work for you
4. Complaining is rocking the boat; don't do that unless you have to
5. Try to get a transfer or job in a less racist place; there are plenty