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Hopefully by now the signs have improved. I would suspect more that she is experiencing irritation or inflammation of the the pharynx or upper airways as a result of the reverse sneezing or maybe from swallowing the rawhide. If the rawhide was stuck or causing an obstruction, we would expect to see more of a gagging or vomiting. Rawhides, even when large pieces are swallowed, will usually soften up and eventually dissolve. I suspect the airways are more of what is involved and if so, with time the irritation should resolve. If she continues to cough however, I would have her examined by your vet to make sure that nothing else is going on.
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