Hi and welcome
! She is just adorable!!!
I hope she continues her success w/ the potties.
As for the rubbing, no, I don't at all think it's allergies as pups this young can't really develop them yet, except for under extremely rare conditions. I think it's more likely just the "puppy itchies"...I think puppies in general scratch more for some reason. And their skin can get dry sometimes too.
You may want to add fish oil or coconut oil to the diet...