Chantel - axolotls can stay in the fridge (according to I.U) for up to 30 days, so yes you can leave her in there for now. Keep her water clean and watch for infection or fungus on her injury. Offer her food daily, but remember in the fridge she will probably not eat as much as she did in the tank.
If her skin is not broken then you do not need to salt bath her.
She was probably bitten by your other axolotls.
You need to make sure your axolotls have lots of hiding places where they can escape each others aggression. Feed them well so they are not as likely to snap at each other in search of food.
Some axolotls are aggressive and don't like sharing their space. As they mature they bully each other for space.
If your axolotls keep fighting you may want to put in tank separators or move them to their own separate tanks.