http://books.google.com/books?id=_REEAAAAMBAJ...

Some people binge up to eight hours and can consume up to 11000 calories per binge. Nevertheless, one striking similarity undercuts all binges — a ...

#1 isn't relevant because it's not 'binge up' as one syntactic group, but 'up to' as one syntactic group, separate from 'binge.'

I read the sentence given in the original post similarly, with 'up inside' as one prepositional idea, inside the body and sort of higher than the abdomen, maybe. It sort of sounds like she's already thinking of it in terms of throwing up.

But if the question is whether there's a BE term 'binge-up,' similar to, say, 'fry-up' or 'knees-up,' then BE speakers will have to answer.

G##gle produces enough hits to show that some people do use "to binge up" to mean "to consume" and others use "a binge up" to mean an act of consumption, in both cases to great excess. In the example given, the use of "up" is ambiguous - it could be indicating location or it could equally be part of "a binge-up".