It sounds like this is a bit more then kennel cough. This sounds more like a full blown upper respiratory infection or even possibly pneumonia , but just coming from a shelter it would be impossible to say if this is bacterial, viral or fungal in nature.
If you can get a thermometer that would be best. If his temp is normal 100.5-102.5 then this can wait until tomorrow to see a regular vet so that you do not have to pay the higher costs of an emergency fee. If his temp is over 103.5 he should be seen right away. I am concerned that the shivering and glassy eyes is due to an elevated body temp.
You could try giving Robitussin DM at a dose of 1 teaspoon per 20lbs to try to help reduce the coughing until morning( only if his temp is normal). I would not give any more ham as this is one meat that does carry risks of causing pancreatitis. What you could try offering is one of the following
Boiled chicken or hamburger ( rinse well after cooking to remove any remaining grease)
Chicken or beef flavored baby food, just make sure there are no onions or garlic in the ingredients.
I would really try to get his temp. If normal I would try to entice him to eat but not force and have him seen by a vet first thing in the morning.
I hope this helps and he feels better soon. Please reply back if you have additional questions and I will be happy to continue. If you have no additional questions please take a few moments to provide a rating so that I am compensated by justanswer for assisting you today.