Hello and thank you for using this site to help you. I am sorry your question was not picked up sooner.
Licking of the paws is a symptom of allergies as is scratching minus the abscence of fleas. With allergies the skin is affected, often dry, which makes the dog scratch.
This can be due to airborne particles, something that came into bloom in the spring, or food allergies. Food allergies usually show some type of rash along the belly and inner thighs.
You can try giving the dog something like zyrtec to help them feel better.
Benadryl is also used, but you don't want to use this if there are any heart problems.
Be sure the medication contains only that for allergies and not the allergy sinus as that contains toxic properties for dogs.
Adding coconut oil to the daily food can also help with allergies and skin issues.
Licking of the carpet can be due to feeling nausea and this can be from the constant licking of the feet and fur.
Below is dosing and information for benadryl and zyrtec
It may take 3-5 days of regular dosing to see the most improvement: http://cheyennewest.com/antihistamines-for-dogs-cats/
coconut oil dosinghttp://sitstay.com/blog/coconut-oil-for-dogs