My first reaction was also that she's crying b/c she's tired. Don't limit her formula, but you may only think she's hungry if she's that tired. Babies like to suck, it really soothes them, so she may act like she's hungry when she's really just tired. My second child was a major sucker...he wanted to suck everything and I mistook it for hunger. My first child was totally not like that and I was confused for probably the first month or so and I fed him too much! ;) But it's okay, seriously, you'd rather err on the side of caution! It is totally fine for her to sleep all day and wake only for a tiny bit. Let her sleep! At this age, I wouldn't wake her to eat unless it's been more than 4 hours (maybe 5 at night).
Why is she awake so much, do you know? Do you have swings, bouncy seats, etc? Do you think she's gassy? Try holding her with her face pointed to the floor and her tummy on your forearm, almost like she's a waitress tray, it could help if she has gas. Also maybe put some fans in the room or other white noise. I've never had to do it but others have told me they used to put their baby in the carrier and put it on top of the washer or dryer to calm their baby.
One month is so young. Do what you have to do to get them to sleep right now. You won't spoil them and you can't hold them too much. In a few months, it's a different story, but right now it's okay to hold them as much as possible and rock them to sleep. Hang in there! I know how hard it is! I hope you have support!