I binged on 2,500cal!

Fasting for two days would be counter-productive and your energy levels and blood sugar would bottom out. I don't think that's the answer. If it were me, I would try to eat lighter for a few days, but say, keep the calories at 1200 a day and restrict carbs and sodium. That way, you will not retain any water.
Dont look upon it as a failure - we all go there from time to time. If you exercise hard, then eat back the exercise calories. You still have to fuel your body each day to cope with what you're doing.
Good luck - just get back on the wagon tomorrow. One day never killed a diet.

Ugh, I can so relate to your situation! That said, the best advice I ever got about trying to eat healthy (especially as a binge eater) was to EAT. THE. NEXT. MEAL. That's it.

The fastest way to get back on track after a binge is to eat your next, healthy meal as if the binge didn't happen. Sure you'll be over your calories -- you would be anyway -- but at least you'll also be getting protein/fibers/fruits-n-veggies in your system vs. all binge food. For me "eating the next meal" also mentally resets my frame of mind to be back on track in my non-bingey healthy eating mode.

Hope that helps. Good luck to you! Sounds like you've been doing great so far so don't beat yourself up too much about this one blip. : )