I'm almost more worried about what's making her drink that much than I am the throwing it up... Because as stressed as she has been, throwing up water right after drinking a lot would be understandable. And I don't think she's throwing up unless I pick her up (which I've been doing only because of the weird pink places and all). But I'm not sure why she's feeling the need to drink that much!
Luckily I can't see any signs of dehydration, or bizarre fluid retention or anything, so I'm holding out hope that this is still due to her skin being so soft and maybe she is losing more water through the skin than would be normal... And her skin is still really soft. The space between the scales seems much larger than normal too. Skin is harder than it was, but still not normal...

It's just so odd because these signs are all pretty worrisome, but whenever I check on her, she sticks her head up and is constantly tongue-flicking and looking around...
I'll post again when I hear back from the vet.