What is the cause of red paws that keep licking?

This indicates that the dog has interdigital toe infection. You can kick the fur off and apply topical antibacterial and anti-inflammatory sprays and creams. Wear an Elizabethan collar, do not allow your dog to lick it, clean and keep the feet dry after going to the grass or going to play during the week, and do not allow your dog to get his toes wet.