Chewing like this on the feet and legs can be due to allergies, fleas, microscopic parasites called mites, skin infection, or to underlying diseases such as hormonal imbalances (adrenal, thyroid), liver disease, etc.
I would start by putting a good effective safe flea product on her, even if you do not see fleas. When dogs become sensitized to flea bites, they only need one flea to see them off scratching all over. I would use Frontline, the Seresto collar, Bravecto, or Nexgard.
For the itching you can try Benadryl, 25 mg for a 25 pound dog 2 to 3 times a day. Supplements like oatmeal wipes or baths, fish oil, anti oxidants, quercetin, and nettles might help.
If none of these make any difference, then she may need skin scrapings to look for microscopic mites, or prescription itch medication such as Apoquel, prednisone, or Temeril P.
It would be best for her to have an exam, basic blood tests, and skin scrapings done, but I understand you took her in and don't have a lot to spend. Start with some good flea medication; about 75% of dog skin problems are related to fleas.
Let me know if this is helpful and what other questions you have.