I am sorry to hear you are worried about Henry. My name is Rebecca. I am a veterinarian and will do my best to help.
It could be the ham. Eating a fatty meal like ham can cause pancreatitis, inflammation of the pancreas, which can cause vomiting, diarrhea, and pain (shaking and panting are signs of pain).
Usually we have to treat pancreatitis with IV fluids and injections to control vomiting and pain. You can't give anything by mouth to treat it, since the pills would be vomited back up and would not be absorbed.
If you check his gums, do they look pale, or pink? If his gums look pale, that is a sign he may be seriously ill and in need of medical care.
If he can't even keep down ice chips or water, he will become dehydrated which will make his condition even worse. I always try to offer home remedies when I can, such as Pepcid AC for vomiting, but this is a case where he needs medical care. He needs to get fluids, an injection of Cerenia for vomiting, possibly antibiotics, and pain medication. If this is pancreatitis, it can be very serious, and I would recommend having him checked by a veterinarian as soon as possible.
Please let me know how he is doing and what other questions you have. Rebecca