With regard to the chewing, you need to crate train her. Put her in her crate at night when you go to sleep and the next morning, the minute you wake up, take her out of the crate and IMMEDIATELY go outside so that she can go to the bathroom. Your walls won't have holes in them, there won't be any pee or poop on the floors and you won't have to use a spray bottle (which is the worst training idea in the history of dogs).
When nobody is home, the dog goes in the crate. As soon as someone comes home, they take her out so she can go toilet. Then she can stay out of the crate as long as someone is home and the family is awake, but at bed time or if the family goes out, she MUST be crated. It is much kinder to crate train her than it is to constantly be reprimanding her because of chewing since within about 15 minutes of chewing she won't have any idea of why she is being yelled at. You can't show them the damage and expect them to make the connection, their minds don't work that way. That's old-school training and it just made for some really neurotic dogs.
What kind of dog is she? At four months of age she shouldn't have any skin conditions unless she has either fleas or she has food allergies. Fleas can be gotten rid of with a good, SAFE product like Advantage or FrontLine TopSpot, or another flea product that you buy FROM YOUR VET. NEVER purchase a flea control product from a department store or food store, these products are extremely dangerous to the health of your pet and most of them don't really work well. Flea collars should also never be used on dogs or cats, truthfully I don't know why the FDA even still allows them to be manufactured and sold.
If it's food allergies, this is going to be a lot harder to control because it's like looking for a needle in a haystack, but the first thing you can try is to feed her something that she has never eaten before. There are pet food companies that make good food in the flavor of Duck and Sweet Potato. If pet has food allergies, oftentimes this flavor of food sits well with them.
Also, look for a pet food that doesn't contain grain. The ingredients list contains the ingredients in order of how much is in the food. If the first ingredient is corn or corn meal, DO NOT buy that food. You need to look for a food that contains MEAT. Dogs are really not built to eat grains so they're really not all that good for them. Dogs can and do eat vegetables, but not so much grains. You can also try a supplement that Omega 3 and Omega 6 oils in it, and give oatmeal baths to soothe the itching.
The only other thing I can suggest for the itching is to tell the vet and see what they want to do to get to the bottom of it. Depending on the breed of dog, some dogs of breeds that have been overbred develop autoimmune problems and they develop these allergies. I am suspecting something like this in her case because she has these problems at such a young age. Please post back and let us know what the vet says with regard to the itching and skin issues.
Can't add much more to what Ghilly advised. I am a firm believer in crate training. All my dogs have been crate trained. What does she have to chew on besides the walls? Have you tried a Kong? As for the itching, yes, that can be a challenge. Take Ghilly's advice on the food. You might try something with fish, grain free. Try feeding that and nothing else. It can take some time to see if there will be a difference. This could be environmental or even an inhalent. Sometimes, your Vet needs to do testing. If this continues, I suggest you consult your Vet.