Yes, your puppy is sick. By the picture, he seems a little light in weight, that is an indication of slight malnutrition, maybe caused by worms. Worms are common and easily treated, afterward the pup usually puts on a little weight,that evenly distributed over the body. The coat is somewhat dulled from lacking nutrition too. Definitely, take your dog to the vet. If you were bleeding from a BM and vomiting, you would go to a doctor, yeah?
Try a better food for helping proper weight maintenance and skin health. Better foods like Nutro, Blue Buffalo, etc are great foods. They cost a little more, but you use less because the companies don't put corn, barley, wheat, and junk fillers to take up space. The more corn and junk the more they eat, and the more bathrooms breaks they need.
Better foods will have the meat listed first followed by potato or a rice or brown rice for the fiber. Potato is way better. The better foods are digested more fully and more nutrients are given to the dog. The better foods fill up the pup quicker and easier. Kind of like when we eat a heavy meal, we are full longer.
Your puppy, you, and your wallet will benefit.