No, absolutely not. That is dangerous especially within smaller breeds. The bones can get stuck and not pass properly through the intestines, or stomach and so forth. They can also get lodged in their throat. They could also cause tearing and other problems if they are sharp. If that happens your dog is going to need an exploratory surgery. I would advise against it. You will spend thousands of dollars and put your pets through a tremendous amount of pain. If you are worried about the teeth, science diet has dental treats. You can give those. They are harder so it good for chewing. They are designed with the intention of helping clean the mouth. Chicken bones are not. Also I would recommend you try brushing and if that doesn’t work at least get the teeth checked once a year to make sure the dog doesn’t develop periodontal disease. Definitely try the science diet dental treats. My dogs love them. They do make a difference.

It could be an allergy of some sort. You won’t know for sure unless you bring him/ her to the vet. You can try using oatmeal shampoo and see if that helps. It could. That also depends on what the allergy is to and the severity of it ( if it is in fact an allergy)