I am sorry to hear that your fellow Buddy is lethargic and has vomited twice after chewing up and likely ingesting part of a jacket sleeve.
I agree that all of these signs are indicative of a possible gastrointestinal obstruction.
In most cases vomiting is triggered by eating something they should not, too much table food, too many treats or something they find to chew on outdoors or around the house.
More serious causes of vomiting in puppies include viral or bacterial infections, a dietary allergy or sensitivity, congenital internal organ failure (kidney or liver disease), or a full or partial gastrointestinal obstruction.
In a young dog, especially one that hasn't finished his vaccine series, a viral infection such as Parvo virus or a foreign body leading to a partial or full gastrointestinal obstruction would be the most likely causes and both can be deadly. Not all dogs with viral infections run a fever initially, sometimes they are too weak to mount a fever response. Worms can cause loose stools, but rarely cause vomiting and lethargy.
With his history of chewing on your jacket and symptoms beginning a day later an obstruction would be the most likely cause.
Because he is young, this has been going on for more than a day, and he is lethargic ideally he would see a veterinarian now. Young puppies dehydrate easily and he needs fluids.
I like to give suggestions to try to help at home but in this case there really isn't anything you can do at home for him now as he is vomiting. He may need emergency surgery, and if this is an obstruction the longer you wait the sicker he will get.
If you don't know of an emergency clinic near you here is a link to help you find one (look under pet emergencies): http://www.vetlocator.com/index.php
Best of luck with your little one.