What do you mean he is vomiting more than normal?
what is normal?
Did he started biting his nails when you switched foods? there could be several reasons why he is doing this. I will say both the vomiting and this combined, you need to go see your vet.
as for rawhides, as far as I can tell they are no good for any dog, bully sticks are better (if you are looking for something similar) or give him actual bones to chew on (I sometimes give my little guys chicken/turkey necks and chicken feet). Not all table food is bad for a dog, it just depends what it is.