did you get your puppy from a breeder? as 10 weeks is a little young and your baby is tiny 12 weeks is more acceptible
here is some info on anemia
Anemia in Dogs
does your dog have any fleas? a little one like that if they get fleas can get anemic
i would not switch any foods just add a little chicken to kibble and rice if you want to encourage eating and also use nutrical and get unflavored pedialyte as well and keep in fridge
what antibiotic are you giving for the kennel cough and are you giving it with food as you have to give 1/2 food antibiotic then 1/2 food as antibiotics on empty stomach will make them sick