Saraub, I'm going to assume you live overseas....India? I only ask because here in North America it would be considered very very strange to propose to a nurse who took care of you in a hospital, and she would definitely say no.
However, I know that outside our culture this is not always abnormal. Perhaps first though, you should go by the hospitsl to see her, and talk to her more? Could you take her to have lunch with you one day and see if she is interested in you as well? Don't worry about marriage just yet....after you have gotten to know her and she seems like a suitable girl, you could discuss the possibility of marriage with her (and both your parents, of course).
Live as if you were to die tomorrow. Learn as if you were to live forever. - Mohandas Gandhi