I'm so sorry, Erin!
I can't imagine how hard it must be to get rid of your dog, I don't think i'd ever be able to do that with ours!
I agree with what BrainGoneBad said about maybe leaving it a few days (if you can cope with the breathing issues) and seeing if your allergies settle down any.
I'm not sure but if I recall, you went a few months/weeks ago to see a dog that you were interested in? Did you have any allergy problems when you went then? Just wondering as if you didn't have any problems then, it might be that this is an allergy to something else and not the dog.
I hope you can get things sorted soon so you can get to feeling better. You are in my thoughts!