About the only thing you can do is take her to a vet to get her on meds. If it's a respiratory problem it's very common and hopefully early enough on that it's treatable. It will only get worse on it's own.
Yes, they can get dehydrated. As long as it has water though I doubt that it would stop drinking unless it is unable to get to the water.
As for her side of her face being poofy, it could just be because sickly rodents often neglect their cleaning rituals because they feel so icky - often giving them a dirty, oily, or poofy look.
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NMGA miniature meat goats, Silver Fox and NZW Rabbits, Muscovy ducks, several breeds of chickens, fancy mice and rats in Michigan