There's an internet mythology that all itching is food allergies -- but many other things should be higher up on th list of potential causes. Food allergies exist (I have a dog with severe ones), but they're much less common than environmental allergies. They actually typically manifest with an inflamed GI tract, not skin itching -- with a true food allergy, you usually get a bright red "stop sign" anus (and all sorts of poop issues). You can lift up the tail and take a good look at the dog's butt--pink is healthy, red is not.
Enviro stuff is much more likely to cause your dog's itching -- especially this time of year (Spring is a tough season for many dogs with enviro allergies). Grass is becoming an increasingly common allergy -- I've lost track of the number of GSDs I've known with grass allergies diagnosed in the last few years.
Parasites and infections also need to be ruled out (usually with a skin scrape). Even simple nutritional deficiencies in EFAs can cause itching -- and adding fish oil helps, eventually, and it's a good idea for most kibble-fed dog since EFAs may not survive heat processing inside kibble, depending when and how they're added to the formula and how long it sits.
I would start at the vet with a skin scrape. If it's inconclusive, or shows some suspicious microbes, my next step would be simply bathing the dog with an antimicrobial veterinary shampoo with chlorhexidene -- it removes allergens and knocks down the opportunistic microbes that set up house on inflamed skin (like staph). It can be used weekly without stripping coat oils (but follow directions on the bottle EXACTLY -- never use it above the shoulders, and keep well away from eyes). Here's an example -- note the reviews about how it's helping allergy dogs:
You can also get chlorhex wipes for the paws whenever the dog comes back inside, if the feet are a major point of irritation.
If your vet isn't sure of the cause, don't hesitate to ask for a referral to a vet derm for help sorting it out though! They know what they're doing in getting to the bottom of skin issue.