People probably aren't observing you as closely as you think. People are often distracted by their own problems.
If you are worried about gossip, you can take a few steps to make yourself less of a target. It can't be avoided entirely, but you can be minimized.
First, don't give out too many details of your personal life. Once that information is out, you can't put it back. Your pets, innocent hobbies and your vacation are safe topics. Don't participate in gossip sessions; have nothing to contribute, and if the conversation continues, suddenly remember that you have something to do elsewere. Never advertise your mistakes or put yourself down in front of anyone. The nurses will not give the reassurance you seek, but will use the information against you.