HI,
As you know you have 2 and maybe 3 issues here. First are the fleas. Flea control is important to you and your pup. Unfortunately flea shampoos are of marginal value since when you rinse off the shampoo, which you must do, you wash away everything that will kill fleas and fleas can jump back on safely. Better is to use a pour on product like Advantage or Frontline. Be sure to treat all dogs and cats in the household to get them under control. Second, the balding areas need to be examined closely. Common causes in young dogs include fleas, ringworm and demodectic mange. Diagnosis is through an exam, skin scraping, or fungal culture. Treatment will depend on the cause. Finally, the vomiting is an issue. Again there are many causes including foreign body ingestion. I would expect an xray to look for someting he may have eaten to begin with and then determine if medication for vomiting is needed. I'm including links to articles for further reading and would suggest finding a new vet to pursue these problems. Best wishes.
http://www.petplace.com/dogs/flea-control-and-prevention-in-dogs/page1.aspx
http://www.petplace.com/dogs/alopecia-in-dogs/page1.aspx
http://www.petplace.com/dogs/vomiting-in-dogs/page1.aspx
Dog Veterinarian
30 years in private practice, 2008 WA State Vet of the Year