Allegies are commom trait for both Labs and Poodles. I did not develop allergies until I was 3. Then I started to scratch and itch all the time and I also will lick my paws.
Sometimes I just lick my paws too because I am bored.. (audible sigh here)! But most of the time it is because I am having a case of the itchies as I call them. My Mom tells me "No Emma" ! But I tell her easy for you to say your paws aren't itching are they? So I will simply say "Ok Mom".. and then go find my hiding spot behind the couch and still do it.. but she always catches me...eek!
She will clean my feet after walks to make sure they are clean and dirt free. If I am licking and seem really bothered she sprays something call "Betagen Spray" . It helps with any infection I might get and ... oohh the relief.. the itching usually stop. So I freely give her my paws to treat :)
I know there are a lot of my Doodle buddies that have it way worse than I do. I urge you to consult with Dermatologist to seek some advice. There is relief out there.