My only advice to you is to hang in there. Things will work out...they ALWAYS end up working out. If you feel like nights aren't for you, don't stay there. I work nights and don't mind it at all. However, I know people that literally get depressed and sick when working nights. I'm sure it's something to do with the circadium rythm.
As for exercise, it's really hard to do when you are working 3 nights a week. I've also gained a little bit of weight. My preceptor constantly offering me candy bars sure isn't helping!! :) What I've found works for me is group fitness classes such as kickboxing, aerobics, and yoga. I find a few a week that fit into my schedule. It's hard for me to do my own workout, but when there is an instructor to motivate me, it is a whole lot easier. If you aren't great at the beginning, keep going back! You'll get better. Even if you only start out with 1 or 2 classes a week, it's something! I can bet it will also make you feel a whole lot better about all aspects of your life, personal and professional.
Good luck, and again, HANG IN THERE!!