Buster was also rubbing his face and licking his paws. I tested him for allergies and he had some environmental and food so I thought that was causing him to rub his face. but when I brought him in for his dental I found out he had cracked the crown off of two teeth from chewing on Bully sticks.
The teeth were exposed so they had to be pulled. He not longer paws at his face...we are still dealing with the food allergies and the occasional flea bite but his symptoms there are more chewing on the paws and rump area. Your baby has such a sweet face and it's so sad he is so miserable with scratching. I hope you can find out the answer.
There is also a saliva allergy test for dogs that can be used to help with elimination diets. It has not been thoroughly reviewed and it is a bit expensive but it can provide a reference for foods that may be trigger foods. It is less invasive than the blood tests and I found out after I got the blood test on Buster that the blood test sometimes gives incorrect readings on food allergies and is better at determining environmental allergies.
NutriScan Food Sensitivity and Intolerance Test for Cats and Dogs - Dr. Dodds