I am sorry to hear you are worried about Doc. I am a veterinarian and will do my best to help.
Is the rawhide bone missing? Did he just chew on it, or did he eat the whole thing?
I have seen rawhide cause "HGE", hemorrhagic gastroenteritis. This is an acute onset of vomiting and diarrhea, with blood in it. Sometimes the dogs are sick enough to need IV fluids until they improve. It could cause an obstruction, but I honestly have not seen a dog get a blockage from rawhide. It is possible, but most of the time rawhide will pass with time.
If he is vomiting, do not try to feed him. Offer only clear fluids like water, broth, or Pedialyte. If he is not vomiting too much, you can try giving Pepcid for vomiting (how much does he weigh? The dose is 5 mg per 10 to 20 pounds of body weight twice daily).
I really like to give dogs with bloody diarrhea the medication metronidazole, but it is not available over the counter. You would need to see his veterinarian for this.
Let me know what else I can help with or answer and how he is doing. Rebecca