Amanda Bynes -- Allegedly Claws Fan in Nightclub ... Then Haunts Bloomies

Amanda Bynes lost it on one of her fans -- during a bizarre 24-hour stretch in NYC -- allegedly assaulting the woman who got too close in a nightclub.

Multiple sources tell TMZ ... Amanda showed up by herself to an event at the Gilded Lily nightclub Monday night in Chelsea. We're told she was dancing alone, wearing sunglasses and keeping to herself ... until random people started taking photos.

At first, Amanda was just yelling at the fans ... but we're told she finally snapped on one woman who claims Bynes spun toward her violently, scratching her neck and arms. Despite the alleged attack ... the woman tells us she's still a fan and doesn't plan to press charges.

Then on Tuesday morning ... several Bloomingdale's shoppers tell us Amanda was limping around the department store for hours with just one shoe while mumbling incoherently.

As we've reported, Bynes' family and friends have been extremely concerned, ... ever since her DUI arrest last month -- and fear something tragic is going to happen before she gets the help she obviously needs.