Golden has been scratching constantly since switching food - food allergy or something else?

my 3 year old golden Hank has been scratching like crazy for the past 6 weeks and it lines up almost exactly with when we switched his food. we went from a brand he'd been on for two years to a new "grain-free salmon" formula because i read grain-free was better. now he's scratching his ears, his paws, his belly - basically anywhere he can reach. he's not bleeding or anything but he's clearly uncomfortable and i feel terrible.

i switched him back to his old food 10 days ago but it hasn't completely stopped yet. is that normal for it to take a while to clear up? and is there a way to figure out what exactly he's allergic to? i've seen people mention elimination diets but i don't really understand how that works or if i need a vet for it.

also curious - is grain-free actually a thing or was that just a trend? i feel like i made things worse trying to do something good for him