Hey Krupa!! I totally understand your struggle girl... :\ But you can still make it!! Try what works best for you. For me, I'm getting up early in the morning and workout from about 6:30 to 7:30 and then my day begins. In the evening I wouldn't be able to do much anyway (like studying, chores etc) so I go to bed at 10:30 pm - yeah, it might sound ridiculously early but for me it's the only way to do something useful at that time and have a good start the next day :)
Of course you're sluggish, work schedule is crazy! Eating right alone wouldn't be enough. I really hope things change soon at your workplace or maybe you'll find a better position somewhere. Best of luck, girl