That is some kind a allergy or has fleas because my puppy has that so I started to get worry because she had it for 3 weeks so I told my dad to take her to the vet and the vet said it was allergy from the fleas so she told us to but a shampoo for her and to rub it in her paws a lot of times like maybe 20 times for each paw and it took of for 10 days I was so happy and then it came back an dmy momo said to wash it with baking soda so then when it was her bath day I rubbed it with baking soda and took the scratching from my dogs paw and biting for ever..
It is just probably itchy my do does the same
Put her back on her regular food and try giving her a bath and leave the shampoo on her for 10 min. Don't let her go outside and stay very long and get her nails clipped.
Is it her pads on her paws that is bothering her? Are they splintering or anything like that?
Id say get her nails clips and its probably skin allergies my sister has a poodle who does the same thing. Sometimes hdrocortisone spray works. (they sell it at walmart for like 4-5 dollars)