Only way to know for sure is to take your dog to a vet. It could be mange, thyroid issues, allergies to mold spores, fleas, or pollen, or several other things. The vet can help you figure out and if you don’t get to the bottom of it she will only get worse over time!
In the mean time you need to get all grains out of this dog’s diet, that includes treats (no sharing corn chips or bread from your sandwich any more!). Find a real pet store (that does not sell puppies) and ask to be directed to the grain-free selection of dog foods. Then start reading labels. You want a product that lists real meat as the first 2 or 3 ingredients, and has no grains. Real meat will be things like lamb, beef, elk, pork, salmon meal, whitefish meal (meal is the entire animal ground up and dried, a good thing). Do not buy any food that lists ‘by-products’ in the ingredients since poultry by-products can be nothing more than chicken feathers!
Next you can help calm the itch and heal the skin with a vinegar and water rinse (1/3 vinegar, 2/3 water). Soak the dog with the mix and allow it to dry in her coat. You might also want to try Witch Hazel with Aloe Vera — find that OTC at any drug store. Pat that on the really raw places a few times each day and allow it to dry.
Vomiting can be caused by her chewing off her hair and swallowing it, or it could be an indication of her underlying condition that is involving her skin. You need to get her to a vet and get her the relief she deserves.
he sounds like he might have bloat. can you get him to an emergency vet?
If he is with you need to find an emergency vet near where ever you are as soon as possible, this could be bloat, or a blockage. Both situations are life threatening. If he is at home you need to have whomever is watching him get him to a vet.