Hello, Mary and welcome!
My name is XXXXX XXXXX it will be my pleasure to assist you and Elliott today.
I'm so sorry to hear that he's not feeling well. From your description, it's possible that he has developed a bacterial or viral infection in his system and has a fever; this is causing the shivering. You can check his temperature if you have a rectal or digital thermometer. Lubricate the end with plain Vaseline or KY Jelly and gently insert into the anus, 1/2 an inch. Hold there for about 2 minutes or until the digital one beeps. Normal body temp. for cats is between 100.5 and 102.5. Also, feel his body to see if it is unusually warm, if you don't have a thermometer. If he has fever over 102.5, you can wipe him down with a cool, damp cloth and apply cool compresses to his belly, groin and underarms. You can still keep him wrapped so he doesn't get a chill. His gums should be light, pearly pink and moist, not sticky. If they are paler, like white or greyish, he needs to be seen by a vet right away.
If he spends any time outside (or even if he's indoor-only), he might have ingested a toxic or other non-food item and this is making him sick. He could have an intestinal obstruction.
If he hasn't used the litterbox all day it may be because he is not eating or drinking much, besides the broth, but it could also indicate that he has a urethral obstruction, which is a medical emergency in male cats. This is a plug in the urethra which doesn't allow him to urinate, so his bladder is full, painful and could burst, if not treated right away. Here is more information for you to read: CLICK
As you can see, there are various possibilities, but due to Elliott's current symptoms and his young age, it would be advisable to have him seen by a vet immediately. If your regular vet doesn't have weekend hours, bring him to the nearest ER vet center for evaluation, diagnosis and treatment. If you need help locating an ER vet, please let me know your city, state and zipcode and I will be happy to help.
I hope all will be well with Elliott!