The other method of testing for allergies is intradermal skin testing. Usually this has to be done at a referral practice, since the allergens are expensive to keep on hand unless they are all used within their expiration dates. For a young dog, properly identifying an allergic disease and appropriate treatment can make a huge difference in comfort over the course of a lifetime. If it is possible for your mom to consider allergy testing it would be worth strong consideration. There are a lot of things that can help reduce itchiness associated with allergies.
Air conditioning helps a lot.
Just running cool water over an itchy dog can relieve the itching for few hours. Aspirin therapy helps some dogs. The most reliable medications for relieving itching are corticosteroids, though. Shedding problems might get better if the itching is reduced but shedding is normal behavior and that makes it hard to control and impossible to eliminate. It really would be a good idea to consider allergy testing, but if it isn't possible your mom can work with your vet to find reasonable solutions to the itchiness.