If she drinks her milk and then points to her cot afterwards it sounds as if she really is hungry. As you mentioned, add a snack during the day (make sure it's not something sugary because this will be burned off quickly and will not satisfy for later). If she keeps waking up at the same time at night then you know it's out of habit.
As for her not sleeping unless you are in the room, it seems you have become a prop. Put her down for a nap and leave the room. Do not go back in unless she is crying (and not just calling your name or whining). If she gets up or tries to get out, go into the room, put her back down and leave. You will definitely meet resistence but unless you want to keep being the prop, you need to fix this now.