Uggg - that sucks. Usually Cleantopia does a good job, but I guess they just didn't pay attention on that one.
I'm not an expert on dresses, but depending on the fabric type, it might not be able to be reshaped.
But if it is able, try to find like a place that specializes in luxury stuff. I'm not sure what hood you live in, but if you go to any sort of fancy or wealthier neighbourhood, there should be plenty of dry cleaners that are used to working with fancy dresses. Hopefully they can just steam it and it'll pop back up. Maybe try looking for something like 명품 세탁소 (luxury drycleaner) but, like, the word 명품 is thrown around very loosely, so be careful.