First, welcome to Pet Talk and THANK YOU FOR ADOPTING!!!!!!

It could be a food allergy or mange. (along with other things it could be)

Was your dog tested for Mange? The vet would do a skin scraping and look at it under a microscope to find out.

Are there areas your dog is scratching more than others?
I ask because with Mange, the dog will itch like CRAZY and will start loosing fur around the edges of the ears and on their elbows first. If it's a food allergy, I think most times it starts with the feet. But every dog could be different.
Maybe try switching foods first to see if it's a food allergy. What food do you feed your pug? If its chicken based, I'd try something without chicken (lamb, salmon, duck... etc)
As far as shampoo, I'd use one with oatmeal.
I speak from experience, My Sierra had mange when I adopted her and she’s allergic to Chicken (does not get itchy… it gives her the runs) and recently I tried switching to a higher quality food and I found out that my Buddy is allergic to something in the food and started itching and chewing on his feet and has lost fur on his feet.

I hope to see pictures of your pug!