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Hello there. My name isXXXXX and I am sorry to hear about your big guy. As long as he is breathing normally otherwise besides coughing/hacking I would not consider it an emergency. Most likely the rawhide is not lodged in his throat anymore but it has caused some irritation/damage to his throat which makes him feel like he has something still caught which results in him still hacking and coughing up white foam. Also as long as he is eating and drinking that is a good sign. I would definitely get him to the vet to make sure everything is ok 100% but in the mean time just monitor him very closely. You can try to feed him a couple pieces of white bread as this has been shown to sooth the throat if something is or was stuck in it.
I hope this helps. Please let me know if you have any additonal questions or concerns. I would be happy to help. Please do not forget to rate my response so I receive credit for my time. thank you!